UPSC Physics Optional PYQs (CSE & IFoS)PYQs

Differentiate between Fresnel and Fraunhoffer diffractions. How can one explain the Fresnel diffraction pattern due to a straight edge?

Give Rayleigh's criterion for resolution. Why telescopes with larger objectives are better? The objective of the telescope at St. Palomer has a diameter of 5.08 m. What is the least distance on Moon which could be resolved by it? (Given distance of moon from the Earth = 3,84,000 km and \lambda = 5890\text{ \AA}).

Why an extended source is necessary to see colours in a soap-film ? Non-reflecting surfaces are made by coating very thin films of a transparent material. Find the maximum thickness of such thin coatings given that \lambda = 5.5 \times 10^{-5}\text{ cm} and \mu = 5/4.

What are the essential conditions for observing the interference of light? Two coherent sources with intensity ratio 4 : 1 interfere. Find I_{\text{max}} / I_{\text{min}}.

Calculate the peak values of \vec{E} and \vec{B} for a laser beam of power 2 \times 10^{10}\text{ W} and radius 0.1 mm.

A short-focus lens is used to focus a laser beam of wavelength 6328 Å. If the beam width is comparable to the focal length of the lens, calculate the area of cross-section of the region of focus.

Write a short note on Ruby laser.

Stale Huygens principle and use it to establish Snell's law of refraction of light. How does this treatment of refraction differ from that given on the basis of Newton's corpuscular theory?

A thin quartz plate for incident light of \lambda = 6100\ \text{\AA} produces, a phase difference (45/4)\lambda between the ordinary and extraordinary rays. What will be the nature of polarisation of the emergent light when plane polarized light of wavelength 4500\text{\AA} is incident on it.

Calculate the minimum plate separation in a Fabry-Perot interferometer to obtain free spectral range of 0.05\text{\AA} in the wave length region 5000\text{\AA}. Calculate also the smallest resolvable wavelength difference for reflectivity of 0.95.

Distinguish between spatial and temporal coherence of light. What kind of coherence is required for interference and diffraction? Explain why it is possible to produce interference effects using two tuning forks of the same frequency but not by two independent sources of light of the same wavelength.

Define dispersive and resolving powers of a plane transmission grating and obtain expressions for the two. Show that the first and second order spectra produced by such a grating will never overlap when the incident light contains wave-lengths in the range 4000\text{\AA} to 7000\text{\AA}.

Explain the terms resolving power and magnifying power of an optical instrument. On what parameter do these physical quantities depend in case of a telescope? For a given re-solving power what is the optimum magnifying power in this case ?

Write a short note on Coupled oscillations.

Write a short note on Ultrasonic.

Consider a resonant cavity of volume V of a container to which a neck of area of cross section a and length l is attached. Show that the product of the square of resonance frequency n and volume V is constant. Comment on the correction needed to the derived relation between n^2 and V. How will you determine this correction?

Write a short note on Phase and group velocities in dispersive media.

A uniform rope of mass M and length L is hanging from a rigid support. A transverse wave travels along the rope. Calculate the speed of the wave at a distance x from the free end the time taken by the wave to travel the whole length.

Write a short note on He-Ne laser.

A 3 MW laser beam which has a diameter of 1\text{ cm} is foccussed by a lens of focal length 5\text{ cm}. The wavelength of laser is 10,000\text{ \AA}. Calculate the intensity of the focal plane of the lens.