UPSC Physics Optional PYQs (CSE & IFoS)PYQs

Define mach number A plane files horizontally at an altitude of 2 km at twice the speed of the sound in air. At what distance from the plane will an observer on the ground first heat it coming?

Describe how fresnel has accounted for the rotation of the plane of polarisation of light. Explain the action of a half-shade device.

Discuss the theory of diffraction grating and find conditions for the absent spectra. Distinguish between resolving power and dispersive power of a grating.

Show that the interference fringes in uncoated thin films are distinct when seen in reflection, but very indistinct in transmission.

Calculate the tension required to generate stationary waves with 4 loops in a string of length 1.0\text{ meter}, and mass 0.30\text{ g.} fixed to a tuning fork vibrating with frequency 200\text{ Hz}.

Write a short note on Holography.

Distinguish between phase velocity and group velocity. Calling group velocity C and phade velocity C in a medium of refractive index n, establish the relation C_g = C \left(1 + \frac{\lambda}{n} \frac{dn}{d\lambda}\right) where \lambda refers to the wavelength of the related light in vacuum

A particle of mass 5g lies in a potential field given by U = (40x^2 + 80)\text{ erg/g}. Determine the frequency and time period of oscillations.

A vibrating source is moving in a medium with speed V_s which is greater than the speed V of propagation of the wave in the medium. Apply Huygens principle to show that a conical wave front of half angle \sin^{-1}\left(\frac{V}{V_s}\right) is generated.

The refractive indices of material of wavelength 5090\text{ \AA}, 5340\text{ \AA} and 5890\text{ \AA} are equal to 1.64, 1.640 and 1.630 respectively. Estimate the phase group velocities of light near \lambda = 5340\text{ \AA}.

Give a mathematical explanation for the production of beats. Calculate the velocity of sound in a gas in which two wave of length 60.0\text{ cm} and 60.6\text{ cm} produce 5 beats per sec.

Explain the general principle of laser action. What do you mean by population inversion ? Discuss the transitions involved in the ruby laser. A pulsed laser is rate at 10\text{mw}. It generates 3\text{ ns} wide pulses at frequency 500\text{ Hz}. Compute the instaneous power in the pulse.

Give an account of the origin of optical activity in eqartz crystal. A wafer of crystalline eqartz of thickness. 2.945 \times 10^{-5}\text{ m} is used to change a beam of linearly polarised light (\lambda = 589\text{ nm}) into circularly polarised light. Find the difference in refractive index for the two waves in the crystal, assuming this to be minimum thickness that will produce the effect.

Write a short note on Formation and reconstruction of hologram.

N coherent oscillation given by \zeta_K a \cos = (\omega t + K \phi) \quad K = 1, 2, 3, \ldots N are added, where a and \phi are independent of K. Deduce the expression for amplitude of the resultant oscillation.

Define coherent length. A helium-neon laser emits radiation at wavelength \lambda = 632.8\text{ nm} with \Delta\lambda = 2\text{ pm}. Calculate the coherence wavelength.

What is Fraunhofer diffraction? Under what conditions may it be observed ? Find an expression for the intensity distribution in double slit Fraunhofer diffraction, taking the result for diffraction at a single slit as given.

An interference pattern is obtained by using two coherent sources of light, and the intensity variation is observed to be \pm 10\% of the average intensity. Determine the relative intensities of the interfering sources.

State Rayleigh Criterison for limit of resolution. Show that \frac{I_{\text{middle}}}{I_{\text{max}}} = \frac{8}{\pi^2}

A particle executing simple harmonic motion, has an acceleration (\pi^2/3)\text{ cm/sec}^2 when the displacement is 1\text{ cm}. Determine the period.