UPSC Physics Optional PYQs (CSE & IFoS)PYQs

Explain the laws of refraction of light on the basis of Huygens principle.

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.

The phase velocity of surface waves of wavelength \lambda is v_p = \left( \frac{2 \pi T}{\lambda \rho} + \frac{g \lambda^{1/2}}{2 \pi} \right) where T is the surface tension and \rho the density of the liquid and g is acceleration due to gravity. Find the group velocity and express it in terms of the phase velocity. For which wavelength is the phase velocity a minimum ?

A particle of mass 10 g lies in a potential given by V(x) = 32 x^2 + 0.2 where x is in metres and V(x) in joules. Write down the equation of motion and solve it. What is the frequency of oscillation?

Write a note on He-Ne laser.

Deduce the possible thickness of a quarter wave plate of quartz which is to be used for sodium light of wavelength 5890 Å, (\mu_o = 1.558, \mu_e = 1.486.)

Define geometrical resolving power of an optical instrument. Derive the expression for the resolving power of a microscope and comment on the relation between resolving power and magnifying power, if any exists.

A sphere of radius a_1 made of a material of density p_1 falls through a fluid with terminal velocity v_1. Another sphere of radius a_2 made of a material of density p_2 falls through the same liquid with terminal velocity v_2. Assuming that the viscous dreg for these particles is given by \pi \eta a v. show that the viscosity of the fluid is given by \frac{2 g a_1^2 a_2^2 (p_2 - p_1)}{9 (a_1^2 v_2 - a_2^2 v_1)}

A body falls from a great height towards the surface of the moon. Write down its equation of motion and solve it to determine the speed with which the body strikes the surface. Also find its numerical value.

Deduce the magnitude and direction of the acceleration of the moon and new moon.

Define differential scattering cross-section for a scattering process, the differential scattering cross-section for neutrons scattered elastically from a solid is of the form \alpha(\theta) = A c^{-B(\vec{K}_i \cdot \vec{K}_f)^2} where A and B are constants and \vec{K}_i and \vec{K}_f are respectively the wave vectors of the incident and scattered neutron. Determine the total scattering cross-section. [\vec{K}_i] = [\vec{K}_f]

An electron with velocity 4 \times 10^6\text{ m/s} approaches a point nucleus from a great distance with an impact parameter 0.5 \times 10^{-10}\text{ m}. Calculate the angular momentum of the electron about the nucleus. Show that the electron scattering is S-wave scattering.

Prove that if E and E' are respectively the neutron energies in the laboratory system, before and after collision with a nucleus of mass number A. then \frac{E'}{E} = \frac{1 + A^2 + 2 A \mu_e}{(1 + A)^2} where \mu_e is the cosine of the scattering angle in the centre of mass system.

Write a note on Addition theorem of velocities in special theory of relativity.

Write a note on Coriolis force.

What is superconductivity? In what kind of materials is it found to occur? Name some parameters which characterise a superconductor. Cite any two major use if we succeed in making superconductors with T_c not far atmospheric temperatures.

Write a brief scientific note on Transistor as an amplifier.

How is a p-n junction prepared? Explain the charge and potential distributions in such a junction in open circuit. Explain how a p-n junction can be used to build a solar cell. Describe the mechanism of the increase of conductivity of Germanium by doping it with Arsenic.

Write a brief scientific note on Logic gates and their applications.

State the laws followed in \alpha-decay by different radioactive nuclei and outline the theory which explained \alpha-decay