UPSC Physics Optional PYQs (CSE & IFoS)PYQs

A three-level laser system emits laser light at a wavelength of 550\text{ nm}. If the population of the upper level exceeds that of the lower level by 25\%, determine the negative temperature characterizing the system.

What do you understand by optical activity? A linearly polarized light is propagating along the optic axis of a quartz crystal of thickness 0.2\text{ cm}. If the difference in the refractive indices corresponding to right circularly polarized and left circularly polarized beams is 7 \times 10^{-5} and the wavelength of the light is 0.5\text{ }\mu\text{m}, calculate the angle of polarization.

Consider a thin lens combination of two convex lenses of focal lengths f_1 = +10\text{ cm} and f_2 = +20\text{ cm}, respectively, separated by 25\text{ cm}. Determine the focal length of the combination and the positions of unit planes.

The diameter of central zone of a zone plate is 2.4\text{ mm}. If a point source of light of wavelength 600\text{ nm} is placed at a distance of 5.0\text{ m} from the zone plate, calculate the position of the first image.

A weakly damped harmonic oscillator consisting of spring-mass system has the following parameters : Mass m = 0.25\text{ kg}, Spring constant k = 100\text{ N m}^{-1}, Damping coefficient \gamma = 1\text{ N s m}^{-1} A periodic force F = 5 \cos \omega t (newton) is applied to the system. Determine (i) the amplitude of the oscillator at resonance and (ii) the Q-value of the oscillator.

Explain the phenomenon of double refraction. What are positive and negative crystals? Give their examples.

The intensity at the central maximum observed on a screen in a double-slit experiment is 2 \times 10^{-3}\text{ W/m}^2. If the path difference between interfering waves reaching a point on the screen is \frac{\lambda}{6}, where \lambda is the wavelength of the light used in the experiment, determine the intensity at that point.

Write down the system matrix for a combination of two thin lenses in paraxial approximation. Hence obtain the focal length of the combination and the positions of unit planes.

A telescope has an objective lens of diameter 10\text{ cm}. Determine whether this telescope can resolve two stars having an angular separation of 2\cdot 4 seconds of arc. (Assume the wavelength of starlight as 550\text{ nm})

Show that the escape velocity V_e on the surface of the Earth is given by V_e = \sqrt{2gR}, where g = 9.8\text{ m/s}^2 and R is the radius of the Earth.

Two satellites A and B of same mass are orbiting the Earth at altitudes R and 5R, respectively, where R is the radius of the Earth. Assuming their orbits to be circular, calculate the ratios of their kinetic and potential energies.

Show that the angular momentum of a rigid body consisting of n particles of masses m_i, i = 1, 2, 3, \dots, n, rotating with an instantaneous angular velocity \mathbf{\omega} about an axis passing through the origin O of the coordinate system OXYZ is given by \mathbf{L} = \mathbf{I} \cdot \mathbf{\omega}, where \mathbf{I} is known as the inertia tensor.

Explain the Poiseuille's equation for the rate of flow of a liquid through a capillary tube. From this, show that if two capillary tubes of radii r_1 and r_2 having lengths l_1 and l_2, respectively, are connected in series, the rate of flow of the liquid is given by Q = \frac{\pi P}{8 \eta} \left( \frac{l_1}{r_1^4} + \frac{l_2}{r_2^4} \right)^{-1} where P is the pressure across the arrangement and \eta is the coefficient of viscosity of the liquid.

Briefly discuss the Kepler's laws of planetary motion.

Consider three inertial frames of reference O, O' and O''. Let O' move with a velocity V with respect to O and O'' move with a velocity V' with respect to O'. Both velocities are in the same direction. Write down the transformation equations relating x, y, z, t with x', y', z', t' and also those relating x', y', z', t' with x'', y'', z'', t''. Hence obtain the relations between x, y, z, t and x'', y'', z'', t''. (The direction of velocity is chosen along the x-axis as per convention)

A charged \pi-meson with rest mass of 273 m_e at rest decays into a neutrino and a \mu-meson of rest mass 207 m_e. Find the kinetic energy of the \mu-meson and the energy of the neutrino. (m_e is the rest mass of the electron)

A particle of mass m\text{ kg} having an initial velocity V_0 is subjected to a retarding force proportional to its instantaneous velocity. Obtain the expression for the velocity and position of the particle as a function of time.

Show that the kinetic energy of a system of n particles is given by T = \frac{1}{2} M V_{\text{cm}}^2 + \frac{1}{2} \sum_{i=1}^n m_i {V'_i}^2 where M is the total mass, V_{\text{cm}} is the velocity of the centre of mass, V'_i is the velocity of the particles about the centre of mass and m_i is the mass of the i\text{th} particle.

State and explain the Hooke's law of elasticity. Briefly discuss the features of stress-strain diagram for the behaviour of a wire undergoing increasing stress.

A galaxy in the constellation Ursa Major is receding from the Earth at 15000\text{ km/s}. If one of the characteristic wavelengths of light emitted by the galaxy is 550\text{ nm}, what is the corresponding wavelength measured by astronomers on the Earth?