UPSC Physics Optional PYQs (CSE & IFoS)PYQs

(i) What is birefringence? Indicate how it can be used to obtain plane and circularly polarized light.

Consider a bare fiber having n_1 = 1\cdot 48 and n_2 = 1\text{ (air)}. Find out the NA. What is the maximum incident angle up to which light can be guided through the fiber?

(ii) Why are the two wavelengths 1\cdot 30\ \mu\text{m} and 1\cdot 55\ \mu\text{m} important in single-mode fiber-optical communication system?

(i) Between multimode and single-mode fibers, explain critically how and why single-mode fiber is chosen for communication.

A slit 0\cdot 25\text{ mm} wide is placed in front of a convex lens and illuminated by plane waves of wavelength 500\text{ nm}. The Fraunhofer diffraction pattern is formed in the focal plane of the lens. In the pattern, the distance from the third minimum on the left to the third minimum on the right is found to be 3\text{ mm}. Find the focal length of the lens.

Consider a system of two thin lenses of focal lengths +15\text{ cm} and -20\text{ cm} separated by a distance of 25\text{ cm} in air. Determine the system matrix. For an object of height 1\text{ cm} placed at a distance of 27\cdot 5\text{ cm} in front of the convex lens, find the size and position of the image.

(ii) Determine its quality factor Q and width of resonance \Delta f.

What are the characteristics of stimulated emission? Show that in the optical region, stimulated emission is negligible compared to spontaneous emission.

Derive the condition for achromatism of two thin lenses separated by a finite distance and made up of same material.

Let E_A = E_1 \sin \omega t \quad \text{and} \quad E_B = E_2 \sin (\omega t + \delta) By using analytical method, obtain an expression to explain interference. Also show that intensity varies along the screen in accordance with the law of cosine square in interference pattern.

Explain the phenomenon of interference in thin films. Why is the contrast better in brightness of fringes obtained from the interference of reflected light rays compared to the transmitted light rays?

Distinguish between high dispersive power and high resolving power.

Obtain an expression for the resolving power of a plane transmission grating. Deduce the missing orders for a double-slit Fraunhofer pattern, if the slit widths are 0\cdot 16\text{ mm} and 0\cdot 8\text{ mm} apart.

At what temperature are the rates of spontaneous and stimulated emission equal? (Assume \lambda = 500\text{ nm})

Show that the plane of polarisation is rotated through \theta = \frac{\delta}{2} = \frac{\pi d}{\lambda} (\mu_L - \mu_R) in optical rotation where symbols have their usual meanings.

A plane-polarised light is incident perpendicularly on a quartz plate cut with faces parallel to optic axis. Find the thickness of the quartz plate which introduces phase difference of 60^\circ between e- and o-rays.

Optical power of 1\text{ mW} is launched into an optical fiber of length 100\text{ m}. If the power emerging from the other end is 0\cdot 3\text{ mW}, calculate the fiber attenuation.

What are the important properties of a hologram?

For stationary waves on a string whose ends are fixed, show that the energy density is maximum at antinodes and minimum at nodes.

Consider an ensemble of two-level atoms in thermal equilibrium. Show that the ratio of Einstein A and B coefficients is given by \frac{A}{B} = \frac{8\pi h \nu^3}{c^3}. Why is it not possible to achieve inversion of population in a two-level medium ?