Search, filter, and study UPSC Civil Services & IFoS Physics past year questions with rigorous derivations, formulas, and step-by-step solutions.
Explain the refractive index distribution for a graded index optical fiber given as \begin{aligned} n^2(r) &= n_1^2 \left[ 1 - 2\delta \left( \frac{r}{a} \right)^q \right], & r < a \\ &= n_1^2 [1 - 2\delta] = n_2^2, & r > a \end{aligned} with usual meaning of symbols. Sketch and name the above profiles with justification for q = 1, 2 and \infty.
Explain physically why dispersion is diminished in multimode parabolic-index fiber than in step-index fiber.
Using the concept of Einstein’s A and B coefficients for a two-level atomic system under thermal equilibrium, determine the ratio of the number of atoms per unit volume in the two levels experiencing spontaneous and stimulated emission. How does the principle of population inversion lead to the gain mechanism in the active medium of the laser?
Find out the angle between the reflected and refracted rays when a parallel beam of light is incident on a dielectric surface at an angle equal to the Brewster's angle. Explain how do you use this concept to produce linearly polarized light.
What is the role of an optical resonator in a laser? Why does one prefer curved mirrors instead of plane mirrors in designing an optical resonator?
With a planoconvex lens of radius of curvature R resting on a plane glass surface, Newton's rings are observed with incident light of wavelength \lambda. Find the radii of m\text{th} order dark rings. What will be the colour of the innermost ring with white light illumination?
In Young's double-slit experiment, a thin mica sheet (refractive index = 1 \cdot 5) is introduced in the path of one of the beams. If the central fringe gets shifted by 0 \cdot 2\text{ cm}, calculate the thickness of the mica sheet. Assume separation between the two slits (d) and between slit and source (D) as d = 0 \cdot 1\text{ cm} and D = 50\text{ cm}.
Explain, with neat diagrams, what you mean by monochromatic spherical aberration with reference to paraxial focus, marginal focus and circle of least confusion.
Using matrix method, find out the equivalent focal length for a combination of two thin lenses of focal lengths f_1 and f_2 separated by a distance a.
A convex lens of focal length 20\,\mathrm{cm} is placed after a slit of width 0.5\,\mathrm{mm}. If a plane wave of wavelength 5000\,\mathring{\mathrm{A}} falls normally on the slit, calculate the separation between the second minima on either side of the central maximum.
Obtain the equation of motion of a simple pendulum using Lagrangian formalism. Hence, obtain expression for the angular frequency of a simple harmonic oscillator.
Find out the phase and group velocities of a radio wave of frequency \omega = \sqrt{2}\omega_p in the ionosphere (as a dielectric medium) of refractive index n = \sqrt{1 - \frac{\omega_p^2}{\omega^2}}. Here, \omega_p is the ionospheric plasma frequency.
The Lagrangian for a particle has the form L = \frac{1}{2} m (\dot{x}^2 + \dot{y}^2) - U(r) Obtain its form in plane polar coordinates and then get expression for the Hamiltonian using appropriate transformation.
A particle of mass m is moving with the velocity \vec{v} on the surface of the earth. Discuss the nature of its motion in both the hemispheres due to the Coriolis force \vec{F} = -2\,m\,\vec{\omega} \times \vec{v}.
How does one obtain the angular velocity of the Earth about the North Pole with respect to a fixed star as 7.292 \times 10^{-5}\,\mathrm{sec}^{-1}? Explain your method of calculating the above value.
Show that the rest mass energy of an electron is 0.51\,\mathrm{MeV}. (use the standard values of the physical parameters).
Prove mathematically that the addition of any velocity of a particle to the velocity of light in free space merely reproduces the velocity of light in free space only.
Write down precisely the conservation theorems for energy, linear momentum, and angular momentum of a particle with their mathematical forms.
Describe briefly the Michelson-Morley experiment and discuss the significance of its null result in the context of the special theory of relativity.
Write down Poiseuille's formula and mention its limitations in analysing the flow of a liquid through a capillary tube.