(a) State the two conditions under which total internal reflection occurs.
(b) A transparent container contains layers of three immiscible transparent liquids A, B and C of refractive indices $n$, $\\frac{3}{4}n$ and $\\frac{2}{3}n$, respectively. A laser beam is incident at the interface between A ...
CBSE CLASS 12 • PHYSICS • CHAPTER 09
Ray Optics and Optical Instruments
244 distinct questions across 347 board paper set appearances (2022–2026).
(a) Using the relation for refraction at a curved spherical surface, derive the expression for lens maker's formula.
(b) Three lenses $L_1$, $L_2$ and $L_3$, each of focal length $40\text{ cm}$, are placed coaxially. The distance between $L_1$ and $L_2$ and between $L_2$ and $L_3$ are $120\text{ cm}...
In an experiment with convex lens of focal length $f$, the screen is fixed at a distance $D$ from the object. A student slowly moves the lens away from the object towards the screen and finds that she is able to form sharp image of the object for two positions of the lens. The distance between these...
(iii) If the distance between object and screen is $80.00\text{ cm}$ and the lens forms sharp images at two positions separated by $20.00\text{ cm}$., the focal length of convex lens is
(A) $15.50\text{ cm}$
(B) $18.75\text{ cm}$
(C) $20.50\text{ cm}$
(D) $22.75\text{ cm}$
A thin plano-convex lens and a thin equi-concave lens are kept coaxially in contact as shown in the figure. Assuming both the lenses are made of glass of refractive index $\mu$, and R is the radius of curvature of each curved surface, the focal length of the combination is :
(A) $\frac{\text{R}}{\mu...
Assertion (A): When a convex lens made of glass is immersed in water, its converging power increases. Reason (R): The focal length of a lens depends only on the radii of curvature of its two faces.
An astronomical telescope consists of two converging lenses. One of them of large aperture and large focal length is called objective lens and the other one, of smaller focal length and smaller aperture is called the eyepiece. It is used to see distant objects which are not seen clearly with naked e...
(a) (i) An object is placed $30\text{ cm}$ from a thin convex lens of focal length $10\text{ cm}$. The lens forms a sharp image on a screen. If a thin concave lens is placed in contact with the convex lens, the sharp image on the screen is formed when the screen is moved by $45\text{ cm}$ from its i...
(a) (i) Draw a ray diagram of a reflecting telescope (Cassegrain) and explain the formation of image. State two important advantages that a reflecting telescope has over a refracting telescope.
(ii) In a refracting telescope, the focal length of the objective is $50$ times the focal length of the ey...
(a) (i) Draw a ray diagram to show the image formation by a compound microscope. Obtain the expression for the total magnification of the microscope when the final image is formed at infinity.
(ii) In a compound microscope, an object is placed at a distance of $1.5\text{ cm}$ from the objective of f...
Assertion (A) : A ray of light is incident normally on the face of a prism. The emergent ray will graze along the opposite face of the prism when the critical angle at glass-air interface is equal to the angle of the prism.
Reason (R) : The refractive index of a prism depends on angle of the prism.
(a) Using the mirror equation and the formula of magnification, deduce that "the virtual image produced by a convex mirror is always diminished in size and is located between the pole and the focus."
OR
(b) A convex lens of focal length $10\text{ cm}$, a concave lens of focal length $15\text{ cm}$...
(a) A parallel beam of light is incident on a face of a prism with refracting angle $60^{\circ}$. The angle of minimum deviation is found to be $30^{\circ}$. The refractive index of the material of the prism is close to :
(A) $1\cdot3$
(B) $1\cdot4$
(C) $1\cdot5$
(D) $1\cdot6$
OR
(b) The angle of...
A double-convex lens, made of glass of refractive index $1\cdot5$, has focal length $10\text{ cm}$. The radius of curvature of its each face, is :
(A) $10\text{ cm}$
(B) $15\text{ cm}$
(C) $20\text{ cm}$
(D) $40\text{ cm}$
Assertion (A) : The image of an object placed between $f$ and $2f$ from a convex lens can be seen on a screen. If the screen is removed, image is not formed.
Reason (R) : Rays from a given point on the object placed between $f$ and $2f$, after passing through a convex lens, do not converge on a poin...
(a) A plano-convex lens of refractive index $\mu_1$ is placed coaxially in contact with a biconcave lens of refractive index $\mu_2$ as shown in the figure. All curved faces are of radius of curvature $R$ each. Obtain the expression for the focal length of the combined lens.
OR
(b) A convex lens is ...
A compound microscope is an optical instrument used for observing highly magnified images of tiny objects. It consists of two convex lenses. The lens near the object is called the objective and the lens near the eye is called the eyepiece. The magnifying power of a compound microscope is given by $m...
A person with normal near point $25\text{ cm}$, using a compound microscope with an objective of focal length $0\cdot8\text{ cm}$ and eyepiece of focal length $2\cdot5\text{ cm}$ can bring an object placed at $0\cdot9\text{ cm}$ from the objective in sharp focus. If the image formed by the objective...
A compound microscope consists of an objective of focal length $2\text{ cm}$ and an eyepiece of focal length $10\text{ cm}$. The eyepiece is kept $20\text{ cm}$ away from the objective. Find the magnifying power of the microscope if the final image is formed at infinity.
(A) $7$
(B) $10$
(C) $14$
(D...
The intermediate image formed in a compound microscope is :
(A) real, inverted and magnified
(B) real, erect and magnified
(C) virtual, erect and magnified
(D) virtual, inverted and magnified
(a) A ray of light is incident on one face of a triangular glass prism of refractive index $n$ and is refracted out from the opposite face. Deduce the expression for refractive index of glass prism in terms of the angle of minimum deviation and angle of the prism. Write the condition on $n$ for refr...
A thin lens is a transparent optical medium bounded by two surfaces, at least one of which should be spherical. Applying the formula for image formation by a single spherical surface successively at the two surfaces of a lens, one can obtain the 'lens maker formula' and then the 'lens formula'. A le...
Which of the following statements is incorrect ?
(A) For a convex mirror magnification is always negative.
(B) For all virtual images formed by a mirror magnification is positive.
(C) For a concave lens magnification is always positive.
(D) For real and inverted images, magnification is always negat...
(a) When a parallel beam of light enters water surface obliquely at some angle, what is the effect on the width of the beam ?
(b) With the help of a ray diagram, show that a straw appears bent when it is partly dipped in water and explain it.
(c) Explain the transmission of optical signal through an...
Assertion (A) : The magnifying power of a compound microscope is negative.
Reason (R) : The final image formed is erect with respect to the object.
A convex lens (n = 1.52) has a focal length of 15.0 cm in air. Find its focal length when it is immersed in liquid of refractive index 1.65. What will be the nature of the lens ?
A point light source rests on the bottom of a bucket filled with a liquid of refractive index $\mu = 1.25$ up to height of $10\text{ cm}$. Calculate :
(a) the critical angle for liquid-air interface
(b) radius of circular light patch formed on the surface by light emerging from the source.
(a) (i) What are the two main considerations for designing the objective and eyepiece lenses of an astronomical telescope ? Obtain the expression for magnifying power of the telescope when the final image is formed at infinity. (ii) A ray of light is incident at an angle of $45^\circ$ at one face of...
Assertion (A): A convex lens, when immersed in a liquid, disappears.
Reason (R): The refractive indices of material of the lens and the liquid are equal.
The focal length of an equiconvex lens
(A) increases when the lens is dipped in water.
(B) increases when the wavelength of incident light decreases.
(C) increases with decrease in radius of curvature of its surface.
(D) decreases when the lens is cut into two identical parts along its principal axi...
(a) A thin convex lens L of focal length $10 \text{ cm}$ and a concave mirror M of focal length $15 \text{ cm}$ are placed coaxially $40 \text{ cm}$ apart as shown in figure. A beam of light coming parallel to the principal axis is incident on the lens. The final image will be formed at a distance o...
(a) (i) Draw a ray diagram for the formation of the image of an object by a convex mirror. Hence, obtain the mirror equation.
(ii) Why are multi-component lenses used for both the objective and the eyepiece in optical instruments?
(iii) The magnification of a small object produced by a compound micr...
A prism is an optical medium bounded by three refracting plane surfaces. A ray of light suffers successive refractions on passing through its two surfaces and deviates by a certain angle from its original path. The refractive index of the material of the prism is given by $\mu = \sin(\frac{A + \delt...
A ray of light is incident normally on a prism ABC of refractive index $\sqrt{2}$, as shown in figure. After it strikes face AC, it will
(A) go straight undeviated
(B) just graze along the face AC
(C) refract and go out of the prism
(D) undergo total internal reflection
(a) Draw a ray diagram to show the formation of an image at the least distance of distinct vision, by a compound microscope. Hence, obtain an expression for its angular magnification.
Beams of red light, blue light, yellow light and violet light are incident on a convex lens, one-by-one. Which one of them converges nearest to the lens ? (i) Blue light (ii) Violet light (iii) Red light (iv) Yellow light
A $5\text{ cm}$ long pencil is placed along the principal axis of a concave mirror of focal length $20\text{ cm}$ such that its nearest end is at a distance of $25\text{ cm}$ from the mirror. Calculate the length of the image of the pencil.
OR
In a Young's double-slit experiment, a beam of light c...
(iv) Consider a convex lens of focal length $15\text{ cm}$. For which of the following values of object-screen distance, two positions of the object can be found to obtain sharp image on the screen ?
(A) $45\text{ cm}$
(B) $50\text{ cm}$
(C) $55\text{ cm}$
(D) $65\text{ cm}$
(a) What are coherent sources ? Why they are necessary for observing stable interference pattern ? Draw a graph showing the variation of intensity of light with the position on the screen in Young's double-slit experiment.
(b) Find the intensity of light at a point on the screen when two interfering...
(a) (i) A point object is kept in front of a convex spherical surface of radius of curvature R. Draw the ray diagram to show the formation of image and derive the relation between the object and image distance (u and v) in terms of refractive index n of the medium and R.
(ii) A convex lens of focal ...
(iv) (a) An astronomical telescope has objective lens and eyepiece of focal lengths $80\text{ cm}$ and $4\text{ cm}$ respectively. To view the image in normal adjustment, the lenses must be separated by a distance of :
(A) $84\text{ cm}$
(B) $76\text{ cm}$
(C) $20\text{ cm}$
(D) $320\text{ cm}$
OR
...
(a) (i) Define refractive index of a medium in terms of speed of light.
(ii) Derive the relation for the refractive index (\mu) of a prism in terms of angle of minimum deviation (\delta_{\text{m}}) and angle of prism (A).
(iii) A ray of light QP is incident normally on the face BC of a triangular ...
33. (a) (i) A parallel beam of monochromatic light falls normally on a single slit of width 'a' and a diffraction pattern is observed on a screen placed at distance D from the slits. Explain :
(I) the formation of maxima and minima in the diffraction pattern, and
(II) why the maxima go on becoming...
(b) An object is placed at a distance of $15\text{ cm}$ from a convex lens of focal length $10\text{ cm}$. On the other side of the lens, a convex mirror is placed coaxially at a distance of $10\text{ cm}$ from the lens. If the image formed by this combination coincides with the object itself, draw ...
The magnification produced by a spherical mirror is $-2.0$. The mirror used and the nature of the image formed will be
(A) Convex and virtual
(B) Concave and real
(C) Concave and virtual
(D) Convex and real
Assertion (A) : In a reflecting telescope, the image does not have chromatic aberration.
Reason (R) : Chromatic aberration occurs only due to refraction of light through an optical medium.
When light travels from an optically denser medium to an optically rarer medium, at the interface it is partly reflected back into the same medium and partly refracted to the second medium. The angle of incidence corresponding to an angle of refraction $90^{\circ}$ is called the critical angle ($i_c...
31. (a) (i) Explain with the help of a labelled ray diagram the formation of final image by an astronomical telescope at infinity. Write the expression for its magnifying power.
(ii) The total magnification produced by a compound microscope is $20$. The magnification produced by the eyepiece is $5$....
OR
If an object in case (i) above is $20\text{ cm}$ from the lens and the screen is $50\text{ cm}$ away from the object, the focal length of the lens used is
(A) $10\text{ cm}$
(B) $12\text{ cm}$
(C) $16\text{ cm}$
(D) $20\text{ cm}$
The distance of an object from first focal point of a biconvex lens is $X_1$ and distance of the image from second focal point is $X_2$. The focal length of the lens is
(A) $X_1\,X_2$
(B) $\sqrt{X_1 + X_2}$
(C) $\sqrt{X_1\,X_2}$
(D) $\sqrt{\frac{X_2}{X_1}}$
A lens is a transparent medium bounded by two surfaces, with one or both surfaces being spherical. The focal length of a lens is determined by the radii of curvature of its two surfaces and the refractive index of its medium with respect to that of the surrounding medium. The power of a lens is reci...
A double-convex lens, with each face having same radius of curvature R, is made of glass of refractive index n. Its power is : (A) $\frac{2(n - 1)}{R}$ (B) $\frac{(2n - 1)}{R}$ (C) $\frac{(n - 1)}{2R}$ (D) $\frac{(2n - 1)}{2R}$
A double-convex lens of power P, with each face having same radius of curvature, is cut into two equal parts perpendicular to its principal axis. The power of one part of the lens will be : (A) 2P (B) P (C) 4P (D) $\frac{P}{2}$
A double-convex lens of power P, with each face having same radius of curvature, is cut along its principal axis. The two parts are arranged as shown in the figure. The power of the combination will be : (A) Zero (B) P (C) 2P (D) $\frac{P}{2}$
For a ray incident at the critical angle, the angle of reflection is :
(A) $0^\circ$
(B) $< 90^\circ$
(C) $> 90^\circ$
(D) $90^\circ$
A ray of light of wavelength $600\text{ nm}$ is incident in water $(n = \frac{4}{3})$ on the water-air interface at an angle less than the critical angle. The wavelength associated with the refracted ray is :
(A) $400\text{ nm}$
(B) $450\text{ nm}$
(C) $600\text{ nm}$
(D) $800\text{ nm}$
(a) (i) Give any two differences between the interference pattern obtained in Young's double-slit experiment and a diffraction pattern due to a single slit. (ii) Draw an intensity distribution graph in case of a double-slit interference pattern. (iii) In Young's double-slit experiment using monochro...
Two media A and B are separated by a plane boundary. The speed of light in medium A and B is $2 \times 10^8 \text{ ms}^{-1}$ and $2.5 \times 10^8 \text{ ms}^{-1}$ respectively. The critical angle for a ray of light going from medium A to medium B is :
(A) $\sin^{-1} \frac{1}{2}$
(B) $\sin^{-1} \frac...
The magnifying power of an astronomical telescope is 24. In normal adjustment, distance between its two lenses is 150 cm. Find the focal length of the objective lens.
(b) In normal adjustment, for a refracting telescope, the distance between objective and eye piece lens is 1.00 m. If the magnifying power of the telescope is 19, find the focal length of the objective and the eyepiece lens.
A thin converging lens of focal length $20 \text{ cm}$ and a thin diverging lens of focal length $15 \text{ cm}$ are placed coaxially in contact. The power of the combination is
(A) $\frac{-5}{6} \text{ D}$
(B) $\frac{-5}{3} \text{ D}$
(C) $\frac{4}{3} \text{ D}$
(D) $\frac{3}{2} \text{ D}$
A lens is a transparent optical medium bounded by two surfaces; at least one of which should be spherical. Applying the formula of image formation by a single spherical surface successively at the two surfaces of a thin lens, a formula known as lens maker's formula and hence the basic lens formula c...
The radii of curvature of two surfaces of a convex lens are $R$ and $2R$. If the focal length of this lens is $\left(\frac{4}{3}\right)R$, the refractive index of the material of the lens is : (A) $\frac{5}{3}$ (B) $\frac{4}{3}$ (C) $\frac{3}{2}$ (D) $\frac{7}{5}$
The focal lengths of the objective and the eyepiece of a compound microscope are $1 \text{ cm}$ and $2 \text{ cm}$ respectively. If the tube length of the microscope is $10 \text{ cm}$, the magnification obtained by the microscope for most suitable viewing by relaxed eye is :
(A) 250
(B) 200
(C) 150...
Explain with the help of a suitable diagram, the phenomenon on which an optical fibre works. Mention any two uses of optical fibres.
(b) A thin equiconvex lens of radius of curvature $R$ made of material of refractive index $\mu_1$ is kept coaxially, in contact with an equiconcave lens of the same radius of curvature and refractive index $\mu_2$ ($>\mu_1$). Find: (i) the ratio of their powers, and (ii) the power of the combinatio...
The focal length of a concave lens is $40\text{ cm}$. The power of the lens is : (i) $0\cdot025\text{ D}$ (ii) $2\cdot5\text{ D}$ (iii) $-0\cdot025\text{ D}$ (iv) $-2\cdot5\text{ D}$
A concave lens of focal length $10\text{ cm}$ is cut into two identical plano-concave lenses. The focal length of each lens will be
(A) $20\text{ cm}$
(B) $30\text{ cm}$
(C) $40\text{ cm}$
(D) $5\text{ cm}$
(a) Draw the ray diagram to show the image formation by a refracting telescope and write the expression for angular magnification for the telescope in normal adjustment.
(b) Give two reasons to explain why a reflecting telescope is preferred over a refracting telescope.
A concave lens of focal length $40\text{ cm}$ is coaxially in contact with two convex lenses, each of focal length $20\text{ cm}$, on each side. The focal length of the combination is
(A) zero
(B) $\frac{20}{3}\text{ cm}$
(C) $-\frac{20}{3}\text{ cm}$
(D) $\frac{40}{3}\text{ cm}$
Draw a labelled ray diagram showing the formation of image by a compound microscope when final image is formed at least distance of distinct vision. Derive an expression for its magnifying power for this case.
(a) Draw a ray diagram to show the image formation by a concave mirror when the object is kept between its focus and the centre of curvature. Using this diagram, derive the mirror formula.
(b) A concave mirror produces a two times magnified virtual image of an object kept $10\text{ cm}$ in front of ...
In an electron microscope, accelerated electrons have wavelength of $0.011\text{ nm}$. Calculate the voltage through which electrons were accelerated to attain this wavelength.
(Take $\text{e} = 1.6 \times 10^{-19}\text{ C}$, $\text{m}_\text{e} = 9 \times 10^{-31}\text{ kg}$, $\text{h} = 6.6 \times ...
(a) Why does one prefer to view the image formed at infinity than that formed at near point in microscope/telescope ?
(b) Consider lenses $L_1$, $L_2$ and $L_3$ as specified in the following table. Which of them will you select as objective and eyepiece for constructing best possible (i) telescope (...
A ray of light is incident on the face of a triangular prism of refracting angle $60^\circ$ and it just suffers total internal reflection at the other face. Find the angle of incidence for the ray if the refractive index of the material of the prism is $\sqrt{2}$.
(iv) Consider a convex lens of focal length $15\text{ cms}$. For which of the following values of object-screen distance, two positions of the object can be found to obtain sharp image on the screen ?
(A) $45\text{ cm}$
(B) $50\text{ cm}$
(C) $55\text{ cm}$
(D) $65\text{ cm}$
(iv) OR A thin convex lens of focal length $10\text{ cm}$ and another thin lens of focal length 'f' are placed coaxially in contact. If the power of their combination is $\frac{10}{3}\text{ D}$, the value of 'f' is
(A) $-15\text{ cm}$
(B) $-10\text{ cm}$
(C) $-20\text{ cm}$
(D) $-30\text{ cm}$
A $5 ext{ cm}$ long pencil is placed along the principal axis of a concave mirror of focal length $20 ext{ cm}$ such that its nearest end is at a distance of $25 ext{ cm}$ from the mirror. Calculate the length of the image of the pencil.
OR
In a Young's double-slit experiment, a beam of light consis...
OR
(iv) A thin convex lens of focal length $10\text{ cm}$ and another thin lens of focal length '$f$' are placed coaxially in contact. If the power of their combination is $\frac{10}{3}\text{ D}$, the value of '$f$' is
(A) $-15\text{ cm}$
(B) $-10\text{ cm}$
(C) $-20\text{ cm}$
(D) $-30\text{ cm}$
33. (a) What are coherent sources ? Why they are necessary for observing stable interference pattern ? Draw a graph showing the variation of intensity of light with the position on the screen in Young's double-slit experiment.
(b) Find the intensity of light at a point on the screen when two interfe...
A girl standing $6\cdot0\text{ m}$ from a convex mirror sees her virtual image $1\cdot0\text{ m}$ behind the mirror. The focal length of the mirror is :
(A) $6\cdot0\text{ m}$
(B) $1\cdot2\text{ m}$
(C) $2\cdot4\text{ m}$
(D) $0\cdot8\text{ m}$
What is meant by linear magnification of an image formed by a spherical mirror ? Write an expression for the magnification produced by a concave mirror in terms of the object distance and the image distance.
A thin convex lens of focal length $25 \text{ cm}$ is cut into two pieces $0.5 \text{ cm}$ parallel and above the principal axis. An object is placed at a distance of $50 \text{ cm}$ in front of the smaller part. Find : (i) the position of the image, and (ii) the magnification produced by this part.
(a) (i) Explain the phenomenon of total internal reflection. State two conditions that must be satisfied for total internal reflection to occur. Derive the relation between the critical angle and the refractive index of a medium.
(ii) A ray of light is travelling from a denser medium of refractive index 1.5 to a rarer medium of refractive index 1.0. Calculate critical angle for total internal reflection.
The process that allows light to travel through a tube which is not straight is -
(A) reflection of light
(B) dispersion of light
(C) scattering of light
(D) total internal reflection
(a) A ray of light travelling along the principal axis is incident on a spherical mirror and reflected back along the same path. Explain, why ?
OR
(b) Write all the sign convention followed for a convex lens.
(a) Briefly explain the working of a reflecting type telescope. Write its two advantages over a refracting telescope. (b) A telescope consists of two lenses of focal length $125 \text{ cm}$ and $5 \text{ cm}$. Find its magnifying power when final image is at (i) infinity (ii) at a distance of $25 \t...
A telescope has an objective lens of focal length 144 cm and an eyepiece of focal length 6.0 cm. The magnifying power and the length of telescope tube will be respectively :
(A) 24, 150 cm
(B) 42, 138 cm
(C) 24, 138 cm
(D) 42, 150 cm
In which of the following, total internal reflection does not occur ?
(A) Twinkling of stars
(B) Brilliance of diamonds
(C) Optical fibre
(D) Reflecting prism
A ray of light is travelling through a rectangular glass slab $refractive index \frac{3}{2}$ and is incident on the horizontal glass-air surface at the critical angle for the two media. The slab is then brought in contact with water $refractive index \frac{4}{3}$ such that a thin horizontal layer of...
An equiconvex lens of focal length 15 cm is cut into two equal plano-convex halves. The focal length of each half will be :
(A) 30 cm
(B) 20 cm
(C) 15 cm
(D) 7.5 cm
A plano-convex lens, made of glass (n = 1.5) has a curved surface whose radius is 40 cm. The image formed of an object is of the same size as that of the object. The distance of the object from the lens is :
(A) 40 cm
(B) 80 cm
(C) 160 cm
(D) 200 cm
Draw a labelled ray diagram of an astronomical telescope when final image is formed at infinity. Write the expression for its magnifying power.
Define the term ‘critical angle’. A small bulb is placed at the bottom of a tank containing a liquid of refractive index $\mu$ at a depth H. It is observed that the light emerges from a circular area of radius r of the surface. Obtain the expression for r in terms of H and $\mu$.
(ii) A convex lens of focal length of 20 cm is used to form the image of an object placed 30 cm away from the lens. Find the position and nature of the image formed.
OR
(b) (i) Two thin converging lenses of focal length $f_1$ and $f_2$ are placed coaxially in contact. Derive expression for the focal...
A ray of yellow light undergoes total internal reflection when it is incident at the interface of two media. This ray is successively replaced by the ray of blue, green and red lights. Which of the following statements is true if the angle of incidence is same in all cases ?
(A) Total internal refle...
A ray of light is incident at angle of $45^{\circ}$ on one face of a prism with an equilateral triangular base. If it passes symmetrically through the prism, find the :
(a) angle of minimum deviation for the prism, and
(b) refractive index of the material of the prism.
Which of the following statements is not correct for this telescope ?
(A) The focal length of objective lens ($f_0$) is larger than the focal length of eyepiece ($f_e$).
(B) Its magnifying power can be increased by increasing the focal length of objective lens ($f_0$).
(C) The distance between two l...
An astronomical telescope has objective lens and eyepiece of focal lengths $80\text{ cm}$ and $4\text{ cm}$ respectively. To view the image in normal adjustment, the lenses must be separated by a distance of :
(A) $84\text{ cm}$
(B) $76\text{ cm}$
(C) $20\text{ cm}$
(D) $320\text{ cm}$
OR
Consider the telescope described in question (iv) (a). Its magnifying power in normal adjustment will be :
(A) $320$
(B) $84$
(C) $76$
(D) $20$
(a) (i) Define refractive index of a medium in terms of speed of light.\n\n(ii) Derive the relation for the refractive index ($\mu$) of a prism in terms of angle of minimum deviation ($\delta_{\text{m}}$) and angle of prism (A).\n\n(iii) A ray of light QP is incident normally on the face BC of a tri...
A convex lens of refractive index $1\cdot 5$ has a focal length of $20\text{ cm}$ in air. Find its nature and focal length when it is immersed in a transparent liquid of refractive index $1\cdot 25$.
(ii) The magnification produced by the telescope does not depend upon the :
(A) colour of light
(B) focal length of objective lens
(C) focal length of eyepiece
(D) apertures of objective lens and eyepiece
(iii) Which of the following statements is \textbf{\textit{not}} correct for this telescope ?
(A) The focal length of objective lens ($f_0$) is larger than the focal length of eyepiece ($f_e$).
(B) Its magnifying power can be increased by increasing the focal length of objective lens ($f_0$).
(C) Th...
Two thin lenses of focal length $f_1$ and $f_2$ are placed in contact with each other coaxially. Prove that the focal length $f$ of the combination is given by $f = \frac{f_1 f_2}{f_1 + f_2}$.
(a) (i) A parallel beam of monochromatic light falls normally on a single slit of width '$a$' and a diffraction pattern is observed on a screen placed at distance $D$ from the slits. Explain :
(I) the formation of maxima and minima in the diffraction pattern, and
(II) why the maxima go on becoming w...
Derive an expression for refractive index of an equilateral prism in terms of the angle of minimum deviation and the angle of the prism. Plot a graph to show the variation of the angle of deviation as a function of angle of incidence.
(a) Draw a labelled ray diagram of a refracting telescope in normal adjustment. Briefly explain its working.
(b) Why is the eyepiece of a telescope of short focal length, while the objective is of large focal length ? Explain.
(b) An object is placed at a distance of $15 ext{ cm}$ from a convex lens of focal length $10 ext{ cm}$. On the other side of the lens, a convex mirror is placed coaxially at a distance of $10 ext{ cm}$ from the lens. If the image formed by this combination coincides with the object itself, draw the...
The focal lengths of the objective and the eyepiece of a compound microscope are $2\text{ cm}$ and $3\text{ cm}$ respectively. If they are kept $25\text{ cm}$ apart, the tube length of the microscope is :
(A) $23\text{ cm}$
(B) $22\text{ cm}$
(C) $20\text{ cm}$
(D) $30\text{ cm}$
(a) The distance of an object from a concave mirror is increased from $12\text{ cm}$ to $15\text{ cm}$. It is observed that the new image becomes $\left(\frac{2}{5}\right)^{\text{th}}$ the size of the initial image. Calculate the focal length of the mirror.
(b) A light ray is incident on the horizon...
A thin convex lens with its two surfaces of radii of curvature $R_1$ and $R_2$ is made of a material of refractive index $\mu_2$. A medium of refractive index $\mu_1$ ($< \mu_2$) surrounds it. Using a ray diagram, derive the Lens Maker's formula when a point object placed on the principal axis in fr...
Two thin converging lenses of focal lengths $f_1$ and $f_2$ are placed coaxially in contact. Draw a ray diagram to show the image formation by the combination. Hence, derive the expression for the focal length of the combination.
Two converging lenses $ ext{L}_1$ and $ ext{L}_2$, of focal lengths $144\text{ cm}$ and $6\text{ cm}$ respectively, are arranged coaxially in a tube $147\text{ cm}$ apart. The arrangement is used to view a far off tree, keeping the eye close to $ ext{L}_2$.
(i) Draw the ray diagram depicting image f...
A glass prism has internal angles of $45^{\circ}$, $45^{\circ}$ and $90^{\circ}$. The glass has a critical angle of $45^{\circ}$. Which of the following ray diagrams depicts the possible path the of light through the prism?
(A)
(B)
For VI-Candidates
Light passes from a certain medium into air. The critical angle of the given medium is $\Theta$, which of the following expressions gives the speed of light in the given medium? Where c is the speed of light in air.
(A) $\frac{1}{c \sin\Theta}$
(B) $\frac{\sin\Theta}{c}$
(C) $\frac...
Assertion (A): The critical angle of light passing from glass to air is minimum for violet colour.
Reason (R): The wavelength of blue light is greater than the light of other colours.
A compound microscope consists of an objective lens of focal length $0.82\text{ cm}$ and an eyepiece lens of focal length $2.9\text{ cm}$. An object is placed $0.91\text{ cm}$ from the objective lens. The image is formed at the near point ($25\text{ cm}$) from the eye.
(I) Calculate that the angula...
(A) Derive lens maker's formula.
(B) Equi-convex lenses are to be manufactured from a glass of refractive index $1.55$, with both faces of the same radius of curvature. What is the radius of curvature required if the focal length is to be $10\text{cm}$?
OR
(A) Define angle of deviation in a prism?
(...
(a) (i) An equilateral triangular prism is made of material of refractive index $\sqrt{2}$. Find the value of the angle of minimum deviation for the prism. How will this value be affected when the prism is immersed in water ?
(ii) A ray of light is incident normally on one face of this prism. Find the minimum angle at which the ray must be incident on the adjacent face inside the prism so that the ray experiences total internal reflection at this face.
An equiconvex lens is made of glass of refractive index $1.55$. If the focal length of the lens is $15.0 ext{ cm}$, calculate the radius of curvature of its surfaces.
The magnification produced by a spherical mirror is $-2\cdot0$. The mirror used and the nature of the image formed will be
(A) Convex and virtual
(B) Concave and real
(C) Concave and virtual
(D) Convex and real
Find the focal length of plano-convex lens of refractive index $1\cdot 5$ and radius of curvature $10\text{ cm}$ when it is immersed in a liquid of refractive index $1\cdot 25$.
The two surfaces of a biconvex lens are of radius of curvature 'R' each. Obtain the condition under which its focal length 'f' be equal to 'R'. If one of the two surfaces of this lens is made plane, what will be the new focal length of the lens ?
A compound microscope has an objective and an eyepiece of focal lengths $f_o$ and $f_e$, respectively. To obtain a large magnification of a small object, the microscope should have :
(A) $f_o$ and $f_e$ small, and $f_e > f_o$
(B) $f_o$ and $f_e$ small, and $f_o > f_e$
(C) $f_o$ and $f_e$ large, and ...
(b) (i) Write any two advantages of a compound microscope over a simple microscope. Draw a ray diagram for the image formation at the near point by a compound microscope and explain it.
(ii) A thin planoconcave lens with its curved face of radius of curvature $R$ is made of glass of refractive index...
Draw a ray diagram showing the image formation when a concave mirror produces a real, inverted and magnified image of an object and hence obtain the mirror formula.
Assertion (A) : In a reflecting telescope, the image does not have chromatic aberration.\nReason (R) : Chromatic aberration occurs only due to refraction of light through an optical medium.
(a) (i) Explain with the help of a labelled ray diagram the formation of final image by an astronomical telescope at infinity. Write the expression for its magnifying power.
(ii) The total magnification produced by a compound microscope is $20$. The magnification produced by the eyepiece is $5$. Whe...
The angle of minimum deviation for a ray of light incident on a thin prism, made of crown glass ($n = 1\cdot52$) is $D_m$. If the prism was made of dense flint glass ($n = 1\cdot62$) instead of crown glass, the angle of minimum deviation will :
(A) decrease by $4%$
(B) increase by $4%$
(C) decrea...
The focal lengths of the objective and the eyepiece of a compound microscope are $f_0$ and $f_e$ respectively. Which of the following statements is correct, in normal adjustment ?
(A) The object is at a distance less than $f_0$ from the objective.
(B) The object is at a distance more than $f_0$ and ...
The focal lengths of the objective and the eyepiece of a compound microscope are $f_{\text{o}}$ and $f_{\text{e}}$ respectively. Which of the following statements is correct, in normal adjustment ?
(A) The object is at a distance less than $f_{\text{o}}$ from the objective.
(B) The object is at a di...
A compound microscope consists of an objective lens of focal length $f_o = 2\cdot0\text{ cm}$ and an eyepiece of focal length $f_e = 6\cdot25\text{ cm}$ separated by a distance of $15\text{ cm}$. How far should an object be placed from the objective so that the final image is formed at infinity ?
(A...
(iv) The focal lengths of the objective and the eyepiece of a compound microscope are $f_o$ and $f_e$ respectively. Which of the following statements is correct, in normal adjustment ?
(A) The object is at a distance less than $f_o$ from the objective.
(B) The object is at a distance more than $f_o$...
(a) Monochromatic light of frequency $5\cdot 0 \times 10^{14} \text{ Hz}$ passes from air into a medium of refractive index $1\cdot 5$. Find the wavelength of the light (i) reflected, and (ii) refracted at the interface of the two media.
OR
(b) A plano-convex lens of focal length $16 \text{ cm}$ is ...
Questions number 29 and 30 are case study-based questions. Read the following paragraphs and answer the questions that follow.
A lens is a transparent medium bounded by two surfaces, with one or both surfaces being spherical. The focal length of a lens is determined by the radii of curvature of its...
A convex lens of focal length '$f$' is cut into two equal parts perpendicular to the principal axis. The focal length of each part will be :
(A) $f$
(B) $2\,f$
(C) $\frac{f}{2}$
(D) $\frac{f}{4}$
The speed of light in two media '1' and '2' are $v_1$ and $v_2$ ($> v_1$) respectively. For a ray of light to undergo total internal reflection at the interface of these two media, it must be incident from
(A) medium '1' and at an angle greater than $\sin^{-1} \left(\frac{v_1}{v_2}\right)$
(B) mediu...
A convex lens of focal length 'f' is cut into two equal parts perpendicular to the principal axis. The focal length of each part will be :
(A) f
(B) 2 f
(C) f/2
(D) f/4
OR
If an object in case (i) above is 20 cm from the lens and the screen is 50 cm away from the object, the focal length of the lens used is
(A) 10 cm
(B) 12 cm
(C) 16 cm
(D) 20 cm
A double convex lens of glass has both faces of the same radius of curvature 17 cm. Find its focal length if it is immersed in water. The refractive indices of glass and water are 1.5 and 1.33 respectively.
A convex lens of focal length 'f' is cut into two equal parts perpendicular to the principal axis. The focal length of each part will be :
(A) f
(B) 2 f
(C) $\frac{f}{2}$
(D) $\frac{f}{4}$
The distance of an object from first focal point of a biconvex lens is $\text{X}_1$ and distance of the image from second focal point is $\text{X}_2$. The focal length of the lens is
(A) $\text{X}_1 \text{ X}_2$
(B) $\sqrt{\text{X}_1 + \text{X}_2}$
(C) $\sqrt{\text{X}_1 \text{ X}_2}$
(D) $\sqrt{\fra...
Two concave lenses $A$ and $B$, each of focal length $8.0 \text{ cm}$ are arranged coaxially $16 \text{ cm}$ apart as shown in figure. An object $P$ is placed at a distance of $4.0 \text{ cm}$ from $A$. Find the position and nature of the final image formed.
The focal length of a concave mirror in air is f. When the mirror is immersed in a liquid of refractive index $\frac{5}{3}$, its focal length will become
(A) $\frac{5}{3} f$
(B) $\frac{3}{5} f$
(C) $\frac{2}{3} f$
(D) $f$
Show the refraction of light wave at a plane interface using Huygens' principle and prove Snell's law.
Two convex lenses A and B, each of focal length 10.0 cm, are mounted on an optical bench at 50.0 cm and 70.0 cm respectively. An object is mounted at 20.0 cm. Find the nature and position of the final image formed by the combination.
The plane face of a planoconvex lens is silvered. The refractive index of material and radius of curvature of the curved surface of the lens are $n$ and $R$ respectively. This lens will behave as a concave mirror of focal length
(A) $\frac{R}{n}$
(B) $\frac{R}{(n - 1)}$
(C) $n R$
(D) $\frac{R}{2(n -...
A light beam converges at a point $\text{O}$. In the path of this beam, a concave lens of focal length $15\text{ cm}$ is placed at a distance of $10\text{ cm}$ before point $\text{O}$. The beam now converges at a point $\text{O}'$. Find the magnitude and the direction of shift $\text{OO}'$.
(a) (i) A thin pencil of length $(f/4)$ is placed coinciding with the principal axis of a mirror of focal length $f$. The image of the pencil is real and enlarged, just touches the pencil. Calculate the magnification produced by the mirror. (ii) A ray of light is incident on a refracting face AB of ...
Two thin lenses of focal lengths $+40 \text{ cm}$ and $-20 \text{ cm}$ and placed coaxially in contact. An object is placed at infinity, in front of the combination. The image formed by the combination will lie —
(A) at a distance of $60 \text{ cm}$, in front of the combination.
(B) at a distance of...
(a) The real image of an object is formed at a distance twice the distance of the object from a concave mirror of focal length $10\text{ cm}$. Find the distance between the object and the image.
OR
(b) An object is placed $1.50\text{ m}$ in front of a lens of power $4.0\text{ D}$. Find the nature an...
(a) State the conditions under which total internal reflection occurs.
(b) A glass slab $3.0\text{ cm}$ thick, is placed over a dark ink dot. Find the height through which the image of the dot is raised. The refractive index of the glass is $1.5$.
OR
(b) (A) A ray of light is incident at an angle of incidence, $\frac{A}{2}$ on face AB of a prism ABC of angle of prism A. The ray emerges normally from the opposite face AC. If the refractive index of the material of the prism be n, find the relation between A and n.
(B) The focal length of a con...
OR
(b) A plano-convex lens of focal length $16\text{ cm}$ is made of a material of refractive index $1\cdot4$. Calculate the radius of the curved surface of the lens.
OR Two convex lenses of focal lengths 60 cm and 20 cm are held coaxially in contact with each other. The power of the combination is : (A) 6.6 D (B) 15 D (C) $\frac{1}{15}$ D (D) $\frac{1}{80}$ D
(a) Monochromatic light of frequency $5.0 \times 10^{14}$ Hz passes from air into a medium of refractive index 1.5. Find the wavelength of the light (i) reflected, and (ii) refracted at the interface of the two media.
OR
(b) A plano-convex lens of focal length 16 cm is made of a material of refracti...
(a) (i) A ray of light passes through a triangular prism. Show graphically, how the angle of deviation varies with the angle of incidence? Hence define the angle of minimum deviation.
(ii) A ray of light is incident normally on a refracting face of a prism of prism angle A and suffers a deviation of...
(iii) The refractive index of the material of a prism is $\sqrt{2}$. If the refracting angle of the prism is $60^\circ$, find (1) Angle of minimum deviation, and (2) Angle of incidence.
(II) (a) If the side AC of the above prism is now surrounded by a liquid of refractive index $\frac{2}{\sqrt{3}}$, as shown in Fig. 2, determine if the light ray continues to graze along the interface AC or undergoes total internal reflection or undergoes refraction into the liquid. (b) Draw the ray...
(for V.I. candidates) A ray of light is incident on an equilateral prism at an angle 3/4 th of the angle of the prism. If the ray passes symmetrically through the prism, find the (a) angle of minimum deviation, and (b) refractive index of the material of the prism.
(I) a) A giant refracting telescope at an observatory has an objective lens of focal length $15\text{ m}$. If an eyepiece of focal length $1.0\text{ cm}$ is used, what is angular magnification of the telescope in normal adjustment?
b) If this telescope is used to view the moon, what is the diameter...
OR
Two media A and B are separated by a plane boundary. The speed of light in medium A and B is $2 \times 10^8 \text{ ms}^{-1}$ and $2.5 \times 10^8 \text{ ms}^{-1}$ respectively. The critical angle for a ray of light going from medium A to medium B is :
(A) $\sin^{-1} \frac{1}{2}$
(B) $\sin^{-1} \f...
(i) Draw a labelled ray diagram of a compound microscope showing image formation at least distance of distinct vision. Derive an expression for its magnifying power.
(ii) A telescope consists of two lenses of focal length 100 cm and 5 cm. Find the magnifying power when the final image is formed at i...
When a ray of light propagates from a denser medium to a rarer medium, it bends away from the normal. When the incident angle is increased, the refracted ray deviates more from the normal. For a particular angle of incidence in the denser medium, the refracted ray just grazes the interface of the tw...
A ray of light of wavelength $600 \text{ nm}$ is incident in water $\left( n=\frac{4}{3} \right)$ on the water-air interface at an angle less than the critical angle. The wavelength associated with the refracted ray is :
(A) $400 \text{ nm}$
(B) $450 \text{ nm}$
(C) $600 \text{ nm}$
(D) $800 \text{ ...
Assertion (A) : In optical fibres, the refractive index of cladding must be lesser than that of the core. Reason (R) : Total internal reflection takes place only when the ray passes from denser to rarer medium.
OR (b) What are optical fibres? How does a light ray travel through an optical fibre? Give two applications of optical fibres.
A glass biconvex lens of focal length $0.6\text{ m}$ and refractive index $1.5$ is immersed in a medium of refractive index $2.0$. Find the new power of the lens and the nature of lens.
(a) (i) Write the relation between u, v and R for a convex spherical surface when refraction takes place from optically rarer to denser medium. Using it, derive 'lens maker formula' for a double convex lens. (ii) Two thin lenses of power $+ 25$ D and $- 5$ D are kept in contact with each other. (1) ...
OR (b) (i) Describe a simple activity to observe diffraction pattern due to a single slit. (ii) The figure below shows an equiconvex lens (of refractive index 1.50) in contact with a liquid layer on top of a plane mirror. A small needle with its tip on the principal axis is moved along the axis unti...
Explain the following : (a) For a simple microscope, the angular size of the object equals the angular size of the image. Yet it offers magnification. (b) Both plane and convex mirrors produce virtual images of objects. Can they produce real images under some circumstances?
The magnifying power of an astronomical telescope is 24. In normal adjustment, distance between its two lenses is $150\text{ cm}$. Find the focal length of the objective lens.
The radii of curvature of two surfaces of a convex lens are $R$ and $2R$. If the focal length of this lens is $\frac{4}{3} R$, the refractive index of the material of the lens is :
(A) $\frac{5}{3}$
(B) $\frac{4}{3}$
(C) $\frac{3}{2}$
(D) $\frac{7}{5}$
OR
(b) A beam of light coming parallel to the principal axis of a convex lens $L_1$ of focal length $16 \text{ cm}$ is incident on it. Another convex lens $L_2$ of focal length $12 \text{ cm}$ is placed coaxially at a distance $40 \text{ cm}$ from $L_1$. The nature and distance of the final image fr...
(a) An air bubble is trapped at point B (CB = 20 cm) in a glass sphere of radius 40 cm and refractive index $\mu = 1.5$ as shown in figure. Find the nature and position of the image of the bubble as seen by an observer at point P. OR (b) In normal adjustment, for a refracting telescope, the distance...
OR A beam of light coming parallel to the principal axis of a convex lens $L_1$ of focal length $16\text{ cm}$ is incident on it. Another convex lens $L_2$ of focal length $12\text{ cm}$ is placed coaxially at a distance $40\text{ cm}$ from $L_1$. The nature and distance of the final image from $L_2...
A beam of light coming parallel to the principal axis of a convex lens $L_1$ of focal length $16 \text{ cm}$ is incident on it. Another convex lens $L_2$ of focal length $12 \text{ cm}$ is placed coaxially at a distance $40 \text{ cm}$ from $L_1$. The nature and distance of the final image from $L_2...
The focal lengths of the objective and the eyepiece of a compound microscope are 1 cm and 2 cm respectively. If the tube length of the microscope is 10 cm, the magnification obtained by the microscope for most suitable viewing by relaxed eye is :
(A) 250
(B) 200
(C) 150
(D) 125
A telescope has an objective lens of focal length $150 \text{ cm}$ and an eyepiece of focal length $5 \text{ cm}$. Calculate its magnifying power in normal adjustment and the distance of the image formed by the objective.
(i) Discuss briefly diffraction of light from a single slit and draw the shape of the diffraction pattern. (ii) An object is placed between the pole and the focus of a concave mirror. Using mirror formula, prove mathematically that it produces a virtual and an enlarged image.
(i) The critical angle for glass is $\theta_1$ and that for water is $\theta_2$. The critical angle for glass-water surface would be (given $_a\mu_g = 1.5$, $_a\mu_w = 1.33$)
(A) less than $\theta_2$
(B) between $\theta_1$ and $\theta_2$
(C) greater than $\theta_2$
(D) less than $\theta_1$
(iii) (a) The critical angle for a ray of light passing from glass to water is minimum for
(A) red colour
(B) blue colour
(C) yellow colour
(D) violet colour
OR
(b) (i) Discuss briefly diffraction of light from a single slit and draw the shape of the diffraction pattern.
(ii) An object is placed between the pole and the focus of a concave mirror. Using mirror formula, prove mathematically that it produces a virtual and an enlarged image.
A thin converging lens of focal length $10\text{ cm}$ is placed coaxially in contact with a thin diverging lens of focal length $15\text{ cm}$. How will the combination behave? Justify your answer.
The critical angle for a ray of light passing from glass to water is minimum for
(A) red colour
(B) blue colour
(C) yellow colour
(D) violet colour
(b) (i) Discuss briefly diffraction of light from a single slit and draw the shape of the diffraction pattern. (ii) An object is placed between the pole and the focus of a concave mirror. Using mirror formula, prove mathematically that it produces a virtual and an enlarged image.
Assertion (A) : Signals through an optical fibre can be transmitted without any appreciable loss of energy.
Reason (R) : An optical fibre works on the principle of total internal reflection.
(a) Name the factors on which focal length of a lens depends. How will a thin biconvex glass lens submerged in water behave? Give reason for your answer.
The power of the combination of two thin convex lenses $L_1$ and $L_2$, kept coaxially in contact, is +10 D. If the focal length of $L_1$ is four times that of $L_2$, find their focal lengths.
(b) (i) Answer the following giving reasons : (1) In modern microscopes, multicomponent lenses are used for both the objective and the eyepiece. (2) In a compound microscope, both the objective and the eyepiece have small focal lengths. (3) When viewing through a compound microscope, our eyes should...
Assertion (A) : Propagation of light through an optical fibre is due to total internal reflection taking place at the core-cladding interface.
Reason (R): Refractive index of the material of the cladding of the optical fibre is greater than that of the core.
Show that the least possible distance between an object and its real image in a convex lens is 4f, where f is the focal length of the lens.
OR
In an astronomical telescope in normal adjustment a straight black line of length L is drawn on the objective lens. The eyepiece forms a real image of this l...
Read the following paragraph and answer the questions that follow.
Types of Lenses and their combination
A convex or converging lens is thicker at the centre than at the edges. It converges a beam of light on refraction through it. It has a real focus. Convex lens is of three types: Double convex le...
Two thin lenses are kept coaxially in contact with each other and the focal length of the combination is 80 cm. If the focal length of one lens is 20 cm, the focal length of the other would be
(a) -26.7cm
(b) 60cm
(c) 80cm
(d) 30cm
Lens generally used in magnifying glass is
(a) single concave lens
(b) single convex lens
(c) combination of convex lens of lower power and concave lens of lower focal length
(d) Planoconcave lens
The magnification of an image by a convex lens is positive only when the object is placed
(a) at its focus F
(b) between F and 2F
(c) at 2F
(d) between F and optical centre
A convex lens of 20 cm focal length forms a real image which is three times magnified. The distance of the object from the lens is
(a) 13.33 cm
(b) 14 cm
(c) 26.66 cm
(d) 25 cm
i. Draw a ray diagram for the formation of image of a point object by a thin double convex lens having radii of curvature $R_1$ and $R_2$. Hence derive lens maker's formula.
ii. A converging lens has a focal length of $10\text{ cm}$ in air. It is made of a material of refractive index $1.6$. If it i...
A glass jug is filled with water to a height of $9.6\text{ cm}$. The depth of a coin lying on its bottom as measured by a microscope is $7.2\text{ cm}$. Find the refractive index of the water and the speed of light in water.
A convex lens is made of the material of refractive index $n_1$. What will happen if it were immersed in a medium of refractive index $n_2$ in the following cases ?
(a) $n_2 > n_1$
(b) $n_2 = n_1$
(a) (i) What is meant by total internal reflection of light ? Write the two conditions necessary for this phenomenon to occur. Briefly explain one of its technological applications.
(ii) A thin converging lens of focal length $10\text{ cm}$ is placed coaxially in contact with a thin diverging lens o...
31. (a) (i) Draw a labelled ray diagram of an astronomical telescope to show the image formation of a distant object by it in normal adjustment. What are the main considerations required in selecting the objective and eyepiece lenses so that the telescope has large magnifying power and high resoluti...
(a) Draw a ray diagram for formation of a real and diminished image of an object kept in front of a concave mirror. Hence derive the mirror equation. (b) A concave mirror of focal length $10 \text{ cm}$ produces a real image which is 3 times the size of the object. Find the distance of the object fr...
(a) Two converging lenses of focal lengths $f_1$ and $f_2$ are placed coaxially in contact. Derive the expression for the focal length of the combination using the ray diagram for the formation of the image of an object by the combination.
(b) The figure shows the variation of image distance $v$ with object distance $u$ for a lens.
(i) What is the nature of the lens ?
(ii) Using the graph, find the focal length of the lens.
(a) (i) Draw a ray diagram to show the formation of image by a concave mirror when the object is placed between f and 2f. Using this diagram, derive the mirror equation.
(ii) An object is kept $30\text{ cm}$ in front of a convex mirror of focal length $12\text{ cm}$. Find the nature and position of...
A thin concave lens of focal length $2\text{f}$ is put in contact with a thin convex lens of focal length 'f'. The focal length of the combination will be :
(a) $2\text{f}$
(b) $\frac{\text{f}}{2}$
(c) $-\text{f}$
(d) $\text{f}$
An equiconvex lens of focal length $f$ is cut into two equal halves perpendicular to its principal axis. Find the focal length of each half of the lens.
When a ray of light passes from a denser to a rarer medium, it bends away from the normal. If we go on increasing the angle of incidence in denser medium, then for a particular value of angle of incidence, the incident ray is refracted along the interface of the two media. This angle is called criti...
Based on the above facts, answer the following questions :
If the refractive index of the denser medium increases, how will the corresponding value of critical angle for the pair of mediums change ?
What is an optical fibre ? Write its two uses.
OR
A ray of light travels from an optically denser medium to a rarer medium and is incident at critical angle ($i_c$). Find the angle of deviation for this ray.
(a) A parallel beam of light of wavelength $600\text{ nm}$ is incident normally on a slit of width $0.2\text{ mm}$. If the resulting diffraction pattern is observed on a screen $1\text{ m}$ away, find the distance of (i) first minimum, and (ii) second maximum, from the central maximum. OR (b) A thin...
For a glass prism of refractive index $\sqrt{3}$, the value of angle of minimum deviation $\delta$ is equal to the angle of prism A. Find the angle of prism A. How will the angle $\delta$ be affected if the prism were immersed in water ?
(a) State the conditions for total internal reflection to take place.
(b) A tank is filled with a transparent liquid to height 'H'. A coin suspended by a thread in the liquid is gradually lowered till it touches the bottom. The apparent depth is determined corresponding to different positions of the...
A converging lens made of glass ($\mu$ = 1.5) has its spherical faces of radii of curvature 10 cm and 20 cm. Find its focal length
(a) in air, and
(b) when it is immersed in a liquid of refractive index 1.25.
The refractive index of an equilateral triangular prism kept in air is $\sqrt{2}$. Calculate: (a) the angle of minimum deviation. (b) the critical angle for the prism.
A biconvex lens made of a transparent material of refractive index 1.25 is immersed in water of refractive index 1.33. Will the lens behave as a converging or a diverging lens? Justify your answer.
Case Study : Read the following paragraph and answer the questions. A number of optical devices and instruments have been designed and developed such as periscope, binoculars, microscopes and telescopes utilising the reflecting and refracting properties of mirrors, lenses and prisms. Most of them ar...
An equiconvex lens forms a two times enlarged real image when an object is kept 16 cm from it. The lens is cut into two identical plano-convex lenses. If the object is again kept 16 cm in front of one of these lenses, then find the nature and position of the image formed.
A ray is incident on a prism of material of refractive index $\sqrt{2}$ at point M such that it grazes along NC after emerging from the prism, as shown in the figure. Find : (a) the critical angle for the prism. (b) the angle of refraction at face AB.
With the help of a ray diagram, show how a compound microscope forms a magnified image of a tiny object, at least distance of distinct vision. Hence derive an expression for the magnification produced by it.
With the help of a ray diagram explain the working of a reflecting telescope. Mention two advantages of a reflecting telescope over a refracting telescope.
A ray of light passes through a prism of refractive index $\sqrt{2}$ as shown in the figure. Find : (i) The angle of incidence ($\angle r_2$) at face AC. (ii) The angle of minimum deviation for this prism.
A ray of light travels from a denser to a rarer medium. After refraction, it bends away from the normal. When we keep increasing the angle of incidence, the angle of refraction also increases till the refracted ray grazes along the interface of two media. The angle of incidence for which it happens ...
For which of the following media, with respect to air, the value of critical angle is maximum ? (a) Crown glass (b) Flint glass (c) Water (d) Diamond
The critical angle for a pair of two media A and B of refractive indices 2.0 and 1.0 respectively is : (a) $0^\circ$ (b) $30^\circ$ (c) $45^\circ$ (d) $60^\circ$
The critical angle of pair of a medium and air is $30^\circ$. The speed of light in the medium is : (a) $1 \times 10^8 \text{ m s}^{-1}$ (b) $1.5 \times 10^8 \text{ m s}^{-1}$ (c) $2.2 \times 10^8 \text{ m s}^{-1}$ (d) $2.8 \times 10^8 \text{ m s}^{-1}$
(a) (i) Define SI unit of power of a lens.
(ii) A plano convex lens is made of glass of refractive index 1.5. The radius of curvature of the convex surface is 25 cm.
(ii.i) Calculate the focal length of the lens.
(ii.ii) If an object is placed 50 cm in front of the lens, find the nature and posit...
The focal length of a concave lens ($\mu_g = 1\cdot5$) in air is $20\text{ cm}$. What should be the refractive index of the surrounding medium so that the lens behaves as a converging lens of focal length $60\text{ cm}$ ? (i) $1\cdot4$ (ii) $1\cdot8$ (iii) $1\cdot7$ (iv) $1\cdot2$
A beam of light coming parallel to the principal axis of a convex lens $L_1$ of focal length $15\text{ cm}$ is incident on it. Another convex lens $L_2$ of focal length $25\text{ cm}$ is placed coaxially at a distance d from $L_1$. For the final image to be formed at infinity, the value of d should ...
The focal length of a concave lens is 40 cm. The power of the lens is :
(i) 0.025 D
(ii) 2.5 D
(iii) - 0.025 D
(iv) - 2.5 D
The focal length of a concave lens ($\mu_g = 1.5$) in air is 20 cm. What should be the refractive index of the surrounding medium so that the lens behaves as a converging lens of focal length 60 cm ?
(i) 1.4
(ii) 1.8
(iii) 1.7
(iv) 1.2
A beam of light coming parallel to the principal axis of a convex lens $L_1$ of focal length 15 cm is incident on it. Another convex lens $L_2$ of focal length 25 cm is placed coaxially at a distance d from $L_1$. For the final image to be formed at infinity, the value of d should be :
(i) 10 cm
(ii...
The focal length of a concave lens ($\mu_{\text{g}} = 1\cdot5$) in air is $20\text{ cm}$. What should be the refractive index of the surrounding medium so that the lens behaves as a converging lens of focal length $60\text{ cm}$ ?
(i) $1\cdot4$
(ii) $1\cdot8$
(iii) $1\cdot7$
(iv) $1\cdot2$
A beam of light coming parallel to the principal axis of a convex lens $\text{L}_1$ of focal length $15\text{ cm}$ is incident on it. Another convex lens $\text{L}_2$ of focal length $25\text{ cm}$ is placed coaxially at a distance d from $\text{L}_1$. For the final image to be formed at infinity, t...
OR (b) (i) What is meant by total internal reflection of light? Write the two necessary conditions for total internal reflection to occur. (ii) Calculate the speed of light in a medium for which the critical angle with respect to air is $45^\circ$.
Answer the following : (a) A convex lens produces a real image of an object. If the upper half of the lens is covered with a black paper, then how will the image be affected? (b) The time difference between the apparent sunrise and the actual sunrise is about $2$ minutes. Explain. (c) Modern telesco...
(d) If a convex lens of focal length 'f' is placed very close to the slit of width 'a' and the screen is kept at the focus of the lens, the size of the central maximum in the diffraction pattern will be :
(i) $\frac{f \lambda}{a}$
(ii) $\frac{2f \lambda}{a}$
(iii) $\frac{f \lambda}{2a}$
(iv) $\frac{...
(a) Define the term 'Power of a lens' and mention its SI unit. (b) A diverging lens is made of a material of refractive index $1\cdot6$. The radii of curvature of its two surfaces are $10 \text{ cm}$ and $30 \text{ cm}$. Calculate its power.
(a) (i) Both the objective and the eyepiece of a compound microscope have short focal lengths. Explain.
(ii) Two convex lenses of focal lengths $1.25\text{ cm}$ and $5.0\text{ cm}$ are used to design a compound microscope with an angular magnification of $30$. Find the required tube length of the mi...
(a) For an equilateral triangular prism, the angle of minimum deviation is $30^\circ$. Find the refractive index of the material of the prism.
(b) The angle of minimum deviation for a prism is found to be equal to the angle of the prism ($A$). Show that the refractive index of the material of the pr...