UPSC Physics Optional PYQs (CSE & IFoS)PYQs

Deduce an expression for the diffraction waves at single slit and discuss how it is related with a Fourier transform.

Write a note on Purity of spectral lines and coherence length.

A soap film of refractive index 1.33 is illuminated with light of different wavelength at an angle of 45^\circ. There is complete destructive interference for \lambda = 5890\text{\AA}. Find thickness of the film.

What is hologram? Explain how the image of the object is formed when one looks through it.

Write a note on Ruby laser.

Explain mathematically how left and right circularly polarized light is produced by combining two linearly polarized beams. Given a beam of light, how can one experimentally test whether it is unpolarized or circularly polarized?

Write a note on Rayleighs criterion and resolving power of a telescope.

Show schematically the intensity distribution for a 2-slit Fraunhofer diffraction-interference, if slit-widths are 2\lambda each and centres of slits have separation 6\lambda. Assume incident light falling normally, and limit the discussion to the central diffraction band range.

A single, slit of width 0.14\text{ mm} is illuminated normally by monochromatic light and diffraction bands are observed on a screen 2\text{ m} away. If the centre of the second dark band is 1.6\text{ cm} from the middle of the central bright band deduce the wavelength of light.

Write down the differential equation for a damped simple harmonic oscillator. Solve it and discuss the characteristics of dead-beat motion.

Nine Kilograms of mercury is poured into a glass U-tube of uniform internal diameter of 1.2\text{ cm}. It oscillates freely about its equilibrium position. Calculate the period of oscillation.

Two transverse sine waves each of amplitude 4\text{ mm} wavelength 2\text{m} and time period 1\text{ s} and in-phase at x=0, t=0 are travelling along the x-axis in opposite directions. Obtain the equation of the resultant wave and comment on its nature. Calculate the maximum displacement at x=2.3\text{ m}. Also locate the antinodes and nodes.

For a certain wave, system the angular velocity \omega and the wave vector k are related as follows: \omega = \omega_0 \left| \sin \frac{k a}{2} \right| \quad \text{for } -\frac{\pi}{a} < k < \frac{\pi}{a} Determine and plot the phase velocity and the group velocity for this system.

For transverse waves passing over a uniform string, prove that the slope of the siring at any position x at a given time is numerically equal to the ratio of the particle speed at that position x and time to the wave speed over the string.

A movable bridge divides sonometer wire into two parts, which differ in length by 1.0 cm and produce 4 beats pre second when sounded together. If the whole length of the wire is 100 cm, find the frequencies of the parts.

How can it be proved experimentally that energy transmission is associated with a wave? The disc of a siren having 60 holes makes 420 revolutions per minute. Find the wavelength of its sound in air 0^\circ\text{C}, if velocity of sound at 0^\circ\text{C} is 332\text{ ms}^{-1}.

Explain the Laser actions in

(i) Helium Neon Laser

(ii) Gas Laser

A beam of lineal polarised light is changed into circularly polarised light by passing it through a slice of double-refracting crystal 0.0030 cm thick. Calculate to difference in the two refractive indices of the crystal, assuming this to be minimum thickness that will produce the result, and that the wavelength is 6 \times 10^{-5}\text{ cm}.

Write a short note on Fraunhofer diffraction by circular aperture.

Write a short note on Rayleigh criterion for resolution.