UPSC Physics Optional PYQs (CSE & IFoS)PYQs

In Michelson interferometer, 100 fringes cross the field of view when the movable mirror is displaced through 0.029\,\text{mm}. Calculate the wavelength of the light source used.

Obtain the conditions for constructive interference and destructive interference in a thin film due to reflected light.

State Huygen's principle. Using this principle and suitable diagram, show that this principle could lead to Snell's law of refraction.

Explain physically why dispersion is diminished in multimode parabolic-index fiber than in step-index fiber.

Explain the refractive index distribution for a graded index optical fiber given as \begin{aligned} n^2(r) &= n_1^2 \left[ 1 - 2\delta \left( \frac{r}{a} \right)^q \right], & r < a \\ &= n_1^2 [1 - 2\delta] = n_2^2, & r > a \end{aligned} with usual meaning of symbols. Sketch and name the above profiles with justification for q = 1, 2 and \infty.

Deduce an expression for resolving power of a diffraction grating, explaining its meaning. What will be the value of the number of slits in the grating to resolve \text{D}_1 and \text{D}_2 lines of sodium in the first order, assuming \lambda and \Delta\lambda respectively as 600\text{ nm} and 0\cdot6\text{ nm}?

Find out the angle between the reflected and refracted rays when a parallel beam of light is incident on a dielectric surface at an angle equal to the Brewster's angle. Explain how do you use this concept to produce linearly polarized light.

Using the concept of Einstein’s A and B coefficients for a two-level atomic system under thermal equilibrium, determine the ratio of the number of atoms per unit volume in the two levels experiencing spontaneous and stimulated emission. How does the principle of population inversion lead to the gain mechanism in the active medium of the laser?

Obtain the equation of motion of a simple pendulum using Lagrangian formalism. Hence, obtain expression for the angular frequency of a simple harmonic oscillator.

Find out the phase and group velocities of a radio wave of frequency \omega = \sqrt{2}\omega_p in the ionosphere (as a dielectric medium) of refractive index n = \sqrt{1 - \frac{\omega_p^2}{\omega^2}}. Here, \omega_p is the ionospheric plasma frequency.

A convex lens of focal length 20\,\mathrm{cm} is placed after a slit of width 0.5\,\mathrm{mm}. If a plane wave of wavelength 5000\,\mathring{\mathrm{A}} falls normally on the slit, calculate the separation between the second minima on either side of the central maximum.

Explain, with neat diagrams, what you mean by monochromatic spherical aberration with reference to paraxial focus, marginal focus and circle of least confusion.

Using matrix method, find out the equivalent focal length for a combination of two thin lenses of focal lengths f_1 and f_2 separated by a distance a.

In Young's double-slit experiment, a thin mica sheet (refractive index = 1 \cdot 5) is introduced in the path of one of the beams. If the central fringe gets shifted by 0 \cdot 2\text{ cm}, calculate the thickness of the mica sheet. Assume separation between the two slits (d) and between slit and source (D) as d = 0 \cdot 1\text{ cm} and D = 50\text{ cm}.

What is the role of an optical resonator in a laser? Why does one prefer curved mirrors instead of plane mirrors in designing an optical resonator?

With a planoconvex lens of radius of curvature R resting on a plane glass surface, Newton's rings are observed with incident light of wavelength \lambda. Find the radii of m\text{th} order dark rings. What will be the colour of the innermost ring with white light illumination?

A left circularly polarized beam (\lambda = 5893^\circ\text{A}) is incident normally on a calcite crystal (with its optic axis cut parallel to the surface) of thickness 0.005141\text{ mm}. What will be the state of polarization of the emergent beam ? Justify your answer. Here the refractive indices for the ordinary and the extraordinary rays are 1.65836 and 1.48641 respectively.

How does the population inversion in an active medium lead to the amplification of light in a laser ? Explain in details.

In a Young double slit experiment, the first bright maximum is displaced by y=2\,\text{cm} from the central maximum. If the spacing between slits and distance from the screen are 0.1\,\text{mm} and 1\,\text{m} respectively, find the wavelength of light.

What are the step index and graded index optical fibers ? What are the conventional optical windows for light propagation through optical fibers ?