UPSC Physics Optional PYQs (CSE & IFoS)PYQs

Explain how inversion of population is achieved in a He-Ne laser.

Calculate the Fraunhofer diffraction pattern from a grating of N slits with width e, separated by equal opaque spaces d. Find the condition for principal maxima and the corresponding values of intensity. A parallel beam of Na light is incident normally on a plane grating with 4250 lines per cm. The second order spectral line is observed to be deviated through 30^\circ. Calculate the wavelength of light.

Let the two waves with parallel electric fields be given by E_1 = 2 \cos \left( \bar{k}_1 \cdot \bar{r} - \omega t + \frac{\pi}{3} \right) \text{kV/m}, E_2 = 5 \cos \left( \bar{k}_2 \cdot \bar{r} - \omega t + \frac{\pi}{3} \right) \text{kV/m}. Find the intensity of each beam I_1, I_2 and also the interference term I_{12} at a point where their path difference is zero. Calculate the visibility V \left( = \frac{I_{\max} - I_{\min}}{I_{\max} + I_{\min}} \right) for the interference pattern. [\epsilon_0 = 8.85 \times 10^{-12} \text{ C}^2/\text{Nm}^2, \mu_0 = 4\pi \times 10^{-7} \text{ N/A}^2]

Find the phase and group velocities for the wave E (z, t) = E_0 \cos (k_1 z - \omega_1 t) + \cos (k_2 z - \omega_2 t) where |k_1 - k_2| \ll k_1 k_2 ; |\omega_1 - \omega_2| \ll \omega_1, \omega_2.

A convex lens of focal length 20 cm and a concave lens of focal length 10 cm are placed 20 cm apart. In between them an object is placed at a distance x from the convex lens. What is the value of x in cm so that the images formed by both of them coincide ?

Consider superposition of two plane polarized electromagnetic waves: E_y = \hat{y} a \cos(kx - \omega t) \text{ and} E_z = \hat{z} b \cos(kx - \omega t + \phi) Discuss the conditions for the resultant wave to be left circularly and right circularly polarized adopting the convention as seen by an observer travelling with the wave.

Define resolving power and dispersive power of a grating. Two spectral lines of wavelengths 500\text{ nm} and 500.5\text{ nm} are seen clearly resolved in second order spectrum of a grating. If the grating has 250 lines per cm, what should be the minimum width of the grating?

The radius of the first zone in a zone plate is 2\text{ mm}. What will be the position of the first image of a point source of light of wavelength \lambda = 500\text{ nm} placed at a distance of 5\text{ m} from the zone plate ?

Describe the working of a Fabry-Perot interferometer. Determine the intensity of the fringes of the transmitted light. Why the fringes obtained in the Fabry-Perot interferometer are comparatively sharper than those obtained from the Michelson interferometer ?

What are chromatic and spherical aberrations Explain. Calculate the longitudinal aberration for rays at a height of 0.01\text{ m} from the principal axis and incident on the cowed surface (radius of curvature = 0.1\text{ m}) of a thin piano-convex lens made of glass (refractive index = 1.5).

Establish the relationship between the phase velocity V_p and the group velocity V_g of waves. Under what physical conditions V_g < V_p, V_g = V and V_g > V_p can be possible ?

How would you produce plane polarized light by reflection ? What is Brewster's law ? Calculate the angular position of the sun above the horizon so that light reflected from a calm lake is completely polarized. The refractive index of water is 1.33. Circularly polarized and unpolarized light are passed in turn through a Nicol prism. The Nicol is rotated about the direction of light as axis. What would you observe in each case ? How would you distinguish between them ?

Derive Snell's law of refraction from fermat's principle. How is the refractive index related to the velocity of light ? Light of wavelength 600 nanometre (in vacuum) enters a glass slab of refractive index 1.5. What are the values of wavelength, frequency and velocity of light in glass ? [Velocity of light in vacuum = 3 \times 10^8\text{ ms}^{-1}]

In the steady state forced vibration a point particle of mass 'm' moves under the influence of an external force (F \sin pt) \hat{i} in addition to the restoring force - (kx) \hat{i} and damping force - (\beta x) \hat{i} . Show that (i) the amplitude is maximum when p = \sqrt{\omega^2 - 2b^2} , where k/m = \omega^2 and (ii) the value of the maximum amplitude is \frac{f}{2b \sqrt{\omega^2 - 2b^2}} . What do you mean by the sharpness of resonance ?

Explain the working of Michelson interferometer using appropriate optical diagram. also draw paths of the rays.

Obtain the relation to find radii of the rings and the wavelength of light in Newton's circular ring. Calculate the radius of curvature of the convex glass surface where diameter of 5^{th} and 15^{th} bright rings formed by sodium yellow light are measured to be 2.303\text{ mm} and 4.134\text{ mm}. Given \mu = 1.5 and \lambda_{yellow} = 5282 \text{\AA}.

The X and Y co-ordinates of Cornu's spiral can be expressed quantitatively by two integrals. Derive the expressions of these integrals.

What is optical activity ? Give reasons for the conclusion that optical rotation in liquids has a molecular origin. What do you mean by ordinary and extraordinary rays ? What are positive and negative crystals ? Give an example of each. Compute the minimum thickness of a quarter-wave plate made from quartz for incident wavelength of 589.3 nanometer. Given \mu_o = 1.544 and \mu_E = 1.553.

4. (a) Why does one get three-dimensional image in holography ? Explain with appropriate figures how can one construct and read a hologram.

Differentiates between Rayleigh and Raman scatterings. Why is Raman scattering considered to be a breakthrough in molecular spectroscopy ? What are the advantages of using laser light in Raman spectroscopy ?