UPSC Physics Optional PYQs (CSE & IFoS)PYQs

What are three and four level pumping schemes ? Explain the lasing action in these with schematic diagrams.

Using Huygens' principle for a plane wave travelling from rarer medium 1 to a denser medium 2, show that \frac{\sin i}{\sin r} = \frac{v_1}{v_2} = \frac{\mu_2}{\mu_1}, where i and r are the angles of incidence and refraction, respectively. v_1, \mu_1 and v_2, \mu_2 are the velocities and refractive indices in media 1 and 2, respectively.

Obtain condition for achromatism of two thin lenses separated by a finite distance. If the dispersive powers of the materials of the two lenses are 0\cdot020 and 0\cdot028, their focal lengths are 10\text{ cm} and 5\text{ cm}, respectively. Calculate the separation between them in order to form achromatic combination.

Write conditions for working of a step-index optical fiber. In a step-index fiber, the core and cladding materials have refractive indices 1\cdot50 and 1\cdot43, respectively. Find the following : (i) Critical propagation angle (ii) Acceptance angle (iii) Total time delay in 1\text{ km} length of the fiber (iv) Total dispersion in 50\text{ km} length of the fiber

(i) What is the difference between Fresnel diffraction and Fraunhofer diffraction ? (ii) What is resolving power of a telescope ? Why is the resolving power of microscope more with UV light than with visible light ?

Write equation for damped harmonic oscillations and obtain expression for logarithmic decrement. In a damped harmonic motion, the first amplitude is 10\text{ cm}, which reduces to 2\text{ cm} after 50 oscillations, each of period 4\text{ seconds}. Determine the logarithmic decrement. Also, calculate the number of oscillations in which the amplitude decreases to 25\%.

Consider the interaction of an electromagnetic wave at the interface of two dielectric media. If electric field \vec{E} is parallel to the plane of incidence, obtain Fresnel's equations and Brewster's law of polarization.

(i) What are the requisite conditions for observation of interference pattern on a screen ? (ii) Derive the expression for fringe width and intensity at a point on the screen in a double slit experiment.

A force \vec{F} is given by \vec{F} = x^2 y \hat{x} + z y^2 \hat{y} + x z^2 \hat{z}. Determine whether or not the force is conservative.

Calculate the gravitational self-energy of the Earth. Given : Mass of Earth M_e = 6 \times 10^{24}\text{ kg} and the Radius of Earth R_e = 6\cdot4 \times 10^6\text{ m}

Define streamline flow of a fluid. Using the equation of continuity for an isotropic fluid, find different components of total energy per unit volume.

What are the consequences of Lorentz transformations on length and time when observed from a frame moving at relativistic velocities ?

(i) Prove that the separation of two colliding particles is same, when observed in centre of mass and laboratory systems. (ii) Determine the kinetic energy of a thin disc of mass 0\cdot5\text{ kg} and radius 0\cdot2\text{ m} rotating with 100 rotations per second around the axis passing through its centre and perpendicular to its plane.

(i) The quantities of rotatory motion are analogous to those of translatory motion. Write the corresponding equations of translatory and rotatory motion. (ii) Describe the theorems of perpendicular and parallel axes in case of a plane lamina.

(i) Derive the expressions for gravitational potentials at a point (I) outside the spherical shell, (II) inside the spherical shell. (ii) Calculate the escape velocity of a body of mass 10\text{ kg} from the surface of Moon \left( g_{\text{Moon}} = \frac{1}{6} g_{\text{Earth}} \right). Mass of Moon = 7\cdot3 \times 10^{22}\text{ kg} Radius of Moon = 1\cdot7 \times 10^6\text{ m}

The wavelength of a prominent X-ray line from a copper target is 0.1512\,\mathrm{nm}. The radiation, when diffracted with (111) plane of a crystal with fcc structure, corresponded to a Bragg angle of 20.2^\circ. If the density of the crystal is 2698\,\mathrm{kg/m^3} and atomic weight is 26.98\,\mathrm{kg/kmol}, calculate the Avogadro number.

Why is the Field Effect Transistor (FET) called Unipolar Transistor? Discuss how it is superior than Bipolar Junction Transistor.

Show that for an n-type semiconductor, the Fermi level lies midway between the donor states and the conduction band edge at low temperature (assuming E_v=0).

Compare the dependence of resistance on temperature of a superconductor with that of a normal conductor. Describe briefly the formation of Cooper pairs.

Why NAND and NOR gates are called universal gates? Give the logic diagram, Boolean equation and the truth table of a X–OR gate.