UPSC Physics Optional PYQs (CSE & IFoS)PYQs

Describe the working principle of a three level solid state laser giving the transitions involved in the laser action.

Write a short note on Holography.

Obtain an expression for the ratio of the probabilities of stimulated and spontaneous emissions. What do you infer from this relation? How is population inversion interpreted thermodynamically?

What is a quarter wave plate? Explain its use in the production and detection of circularly polarized light. For calcite for \lambda = 5472 \text{\AA}, \mu_O = 1.658 and \mu_E = 1.486. If the minimum thickness of a plate that can be cut from calcite is 30 \mu\text{ m}, what should be the minimum thickness for preparing a quarter wave plate?

A fine slit is illuminate by monochromatic light of wave-length 6000 Å. A thin wire is placed parallel to the slit and the diffraction pattern is observed on a screen at a distance of 1 m from the wire. In the shadow of the wire equidistant fringes of thickness 1.5 mm are observed. How do you explain this observation ? Calculate he diameter of the wire also.

The angular separation between two distant stars is 1 arc-second. If the effective wavelength of light is 5500 Å; what should be the diameter of the objective of a telescope so that the stars are just resolved?

Show that the interference fringes obtained in Young's two slit experiment are hyperbolic in shape. Under what conditions these are expected to appear straight?

What is meant by temporal and spatial coherence ? Show that the coherence length L = \lambda Q, where \lambda is the mean wavelength and Q represents the purity of a spectral line.

The potential energy for the interaction between two gas molecules can be represented by the function. \phi(r) = -\phi_0 \left[ 2 \left(\frac{r_0}{r}\right)^6 - \left(\frac{r_0}{r}\right)^{12} \right] Where \phi_0 and r_0 are constant. Prove that for small oscillations the frequency is given by \omega = \left( \frac{144 \phi_0}{m r_0^2} \right)^{1/2} Where m is mass of each molecule.

Write a short note on Fourier transformation.

Write the equation of motion for an oscillator driven by a simple harmonically varying force. Obtain the condition for maximum energy transfer to the oscillator.

Define Coriolis force. Obtain an expression for the Coriolis force. How does it account for the whirling of winds in opposite directions in Northern and Southern hemispheres?

A satellite has apogee and perigee heights above the sumace of earth as 4000 km and 640 km respectively. Calculate the eccentricity of the orbit and semi-major axis. Radius of the earth is 6400 km.

Write a short note on Mass-energy equivalence.

A particle of mass m_1 moving with a velocity v_1 undergoes an elastic collision with a particle of mass m_2 at rest, in laboratory-frame. After the collision the first particle moves at a certain angle to the direction of its initial velocity, and this angle is \theta in laboratory-frame and \phi in centre of mass-frame. If the ratio of masses \left(\frac{m_2}{m_1}\right) is a, show that \theta and \phi are related as \tan \phi = \left(\frac{\sin \phi}{\cos \phi + \frac{1}{A}}\right).

A Particle of mass m, moving with an initial velocity v_0 is acted on by a central repulsive inverse-square force, F = \frac{k}{r^2}. Show that the scattering angle \phi depends on the impact parameter b as \cot \left(\frac{\phi}{2}\right) = \frac{m v_0^2}{k} b.

The coordinates of an event in an inertial frame S are (25\text{ m}, 0, 0, 5 \times 10^{-8}\text{ s}). What will be the coordinates of this event in another interntial frame S' moving with a velocity 0.6 c in + x- direction with respect to S. The origins of the two frames were coincident at t = t' = 0

State Bernoulli's theorem. A horizontal pipe has a cross-section of 10\text{ cm}^2 in one region and 5\text{ cm}^2 in another. The pressure of water in the two regions is 2.370 \times 10^5\text{ N/m}^2 and 1.995 \times 10^5\text{ N/m}^2 respectively. Calculate the amount of water flowing through the pipe per minute.

A spherical body of mass 'm' and radius 'a' is falling through a viscous fluid. If it started from rest and \eta is coefficient of viscosity of the fluid obtain an expression for its velocity as function of time. What is meant by relaxation time ? On what factors will it depend in this case?

Establish the two Barkhausen conditions for sustained sinusoidal oscillations. Sketch the circuit of Wien's bridge oscillator and explain its working.