(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 $120\text{ cm}$ and $20\text{ cm}$ respectively. An object is kept at a distance of $80\text{ cm}$ to the left of lens $L_1$. Find the distance of the final image formed from the object. OR (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 it. Calculate the focal length of the mirror.