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 $5$. When the microscope is focussed on a certain object, the distance between the objective and eyepiece is observed to be $14\text{ cm}$. Calculate the focal lengths of the objective and the eyepiece. (Given that the least distance of distinct vision $= 25\text{ cm}$) OR (b) (i) Two coherent light waves, each of intensity $I_0$ superpose each other and produce interference pattern on a screen. Obtain the expression for the resultant intensity at a point where the phase difference between the waves is $\phi$. Write its maximum and minimum possible values. (ii) In a single slit diffraction experiment, the aperture of the slit is $3\text{ mm}$ and the separation between the slit and the screen is $1\cdot5\text{ m}$. A monochromatic light of wavelength $600\text{ nm}$ is normally incident on the slit. Calculate the distance of (I) first order minimum, and (II) second order maximum, from the centre of the screen.