UPSC Physics Optional PYQs (CSE & IFoS)PYQs

Discuss spatial evolution of Fresnel diffraction into Fraunhofer diffraction.

Explain the lasing action of \text{He}-\text{Ne} laser using energy level diagram and describe the operation of \text{He}-\text{Ne} laser experimental set-up.

Discuss the applications of lasers in communication and medicine.

Classify fibers based on the number of modes that can propagate through them. Depict step-index and graded-index multimode fibers pictorially.

During an earthquake, a horizontal shelf moves vertically. If its motion can be regarded simple harmonic, calculate the maximum value of amplitude of oscillation so that the books resting on it stay in contact with it always. Take g=9.8\ \mathrm{m\,s^{-2}} and T=0.5\ \mathrm{s}.

The displacement associated with a three-dimensional plane wave is given by \Psi(x,y,z,t) = a\cos\left[\frac{\sqrt{3}}{2}kx + \frac{1}{2}ky - \omega t\right]. Calculate the angles made by the propagating wave with the x, y and z-axes.

In a tungsten filament lamp, thermionic emission takes place at 1.2\times10^3\ \mathrm{K}. Calculate the ratio of spontaneous emission to stimulated emission for non-degenerate energy levels. Interpret your result physically. Take \lambda=550\ \mathrm{nm}, k_B=1.38\times10^{-2}\ \mathrm{J\,K^{-1}}, h=6.67\times10^{-34}\ \mathrm{J\,s} and c=3\times10^8\ \mathrm{m\,s^{-1}}.

A parallel beam of light from a He–Ne laser (\lambda=630 nm) is made to fall on a narrow slit of width 0.2\times10^{-3} m. The Fraunhofer diffraction pattern is observed on a screen placed in the focal plane of a convex lens of focal length 0.3 m. Calculate the distance between the

(i) first two minima and

(ii) first two maxima on the screen.

Explain the physical significance of resolving power of a grating with relevant mathematical expression.

Explain why information carrying capacity of an optical fibre can be enhanced by reducing the pulse dispersion. How does one minimize pulse dispersion using a graded index optical fibre?

Show that the kinetic energy and angular momentum of torque free motion of a rigid body is constant.

Calculate the horizontal component of the Coriolis force acting on a body of mass 0.1\ \mathrm{kg} moving northward with a horizontal velocity of 100\ \mathrm{ms^{-1}} at 30^{\circ}\mathrm{N} latitude on the Earth.

Suppose that an S'-frame is rotating with respect to a fixed frame having the same origin. Assume that the angular velocity \vec{\omega} of the S'-frame is given by \vec{\omega}=2t\hat{\imath}-t^{2}\hat{\jmath}+(2t+4)\hat{k} where t is time and the position vector \vec{r} of a typical particle at time t as assumed in S'-frame is given by \vec{r}=(t^{2}+1)\hat{\imath}-6t\hat{\jmath}+4t^{3}\hat{k}. Calculate the Coriolis acceleration at t=1 second.

A particle describes a circular orbit under the influence of an attractive central force directed towards a point on the circle. Show that the force varies as the inverse fifth power of distance.

Prove that as a result of an elastic collision of two particles under non-relativistic regime with equal masses, the scattering angle will be 90^\circ. Illustrate your answer with a vector diagram.

Derive the relativistic length contraction using Lorentz transformation.

Show that a particle of rest mass m_0, total energy E and linear momentum \vec{p} satisfies the relation E^2=c^2p^2+m_0^2c^4 where c is the velocity of light in free space.

Obtain an expression for the angular speed of the Earth at which Coriolis force makes objects fly from its surface.

A satellite revolves in a circular orbit around the Earth at a certain height above it. Calculate the time period of revolution of the satellite, if the radius of the Earth is significantly higher than the height at which the satellite revolves.

If the forces acting on a particle are conservative, show that the total energy of the particle which is the sum of the kinetic and potential energies is conserved.