Search, filter, and study UPSC Civil Services & IFoS Physics past year questions with rigorous derivations, formulas, and step-by-step solutions.
Describe the working of a Fabry-Perot interferometer. Determine the intensity of the fringes of the transmitted light. Why the fringes obtained in the Fabry-Perot interferometer are comparatively sharper than those obtained from the Michelson interferometer ?
Consider superposition of two plane polarized electromagnetic waves: E_y = \hat{y} a \cos(kx - \omega t) \text{ and} E_z = \hat{z} b \cos(kx - \omega t + \phi) Discuss the conditions for the resultant wave to be left circularly and right circularly polarized adopting the convention as seen by an observer travelling with the wave.
Define resolving power and dispersive power of a grating. Two spectral lines of wavelengths 500\text{ nm} and 500.5\text{ nm} are seen clearly resolved in second order spectrum of a grating. If the grating has 250 lines per cm, what should be the minimum width of the grating?
Establish the relationship between the phase velocity V_p and the group velocity V_g of waves. Under what physical conditions V_g < V_p, V_g = V and V_g > V_p can be possible ?
The radius of the first zone in a zone plate is 2\text{ mm}. What will be the position of the first image of a point source of light of wavelength \lambda = 500\text{ nm} placed at a distance of 5\text{ m} from the zone plate ?
What are chromatic and spherical aberrations Explain. Calculate the longitudinal aberration for rays at a height of 0.01\text{ m} from the principal axis and incident on the cowed surface (radius of curvature = 0.1\text{ m}) of a thin piano-convex lens made of glass (refractive index = 1.5).
An unstable particle has a lifetime of 5\text{ }\mu\text{s} in its own frame of reference and is moving towards the earth at a speed of 0.8\text{ C}. What will be the lifetime of the particle to an observer on the earth ?
A body of rest mass m_0 is moving in the positive direction at a velocity of 0.6\text{ C} relative to the laboratory frame. Calculate the components of the four dimensional momentum vector in the laboratory frame and in the frame of an observer who is travelling in the positive x-direction at a speed of 0.8\text{ C} relative to the laboratory frame.
The angular momentum \vec{M} of a rigid body comprising of N particles and rotating with angular velocity \vec{\omega} is given by : \vec{M} = \sum_{k=1}^{N} m_k \vec{r}_k \times (\vec{\omega} \times \vec{r}_k) where the origin coincides with the centre of mass. Express the components of \vec{M} in terms of components of the inertia tensor. Hence, show that the most general free rotation of a spherical top is a uniform rotation about an axis fixed in space.
Write down the Lagrangian of a free particle in rectangular cartesian coordinates. Identify all the cyclic coordinates. Show that the constants of motion obtained from the equations for the considered form of the Lagrangian are not exactly the same as those which follow from the concept of a free particle.
Show, using the above relation, that the equation of motion of the particle in S gets modified in S' giving rise to various fictitious forces. Identify the coriolis force and describe its effect on the flow of rivers.
Derive the relation \vec{v}_0 = \vec{v} + \vec{\omega} \times \vec{r}, where \vec{v}_0 is the velocity of a particle located at \vec{r} in a fixed frame of reference S and \vec{v} that as observed in a frame S' rotating with angular velocity \vec{\omega} with respect to S but having the common origin.
State the postulates of the special theory of relativity and based on these obtain Lorentz as well as inverse Lorentz transformations. Hence, obtain an expression to conclude that a moving clock runs more slowly than a stationary clock.
The following common-emitter amplifier is required to have a signal voltage gain V_{\text{out}} / V_S of at least 100. The transistor has \beta = 63, early voltage V_A = 100\text{ V} and I_{SE} = 1.5 \times 10^{-14}\text{ A} :
Assuming that the operating collector voltage is supposed to be + 6\text{ V}, perform related calculations to check whether the circuit satisfies the operating point and voltage gain criteria. The reactance of the capacitors can be neglected at all frequencies.
What are Brillouin zones ? How are they related to the energy levels of an electron in a metal ? Draw the Brillouin zone for a rectangular lattice of sides \pi and 2\pi. Also compute the energy at the corner and midpoints of the adjacent sides of the first Brillouin zone.
What is a microprocessor ? Explain the internal architecture of an 8085 \mu\text{P}.
Explain the working and applications of a FET.
(i) Simplify the logical expression f = ABC + B \overline{C} D + \overline{A} BC by using Karnaugh map and realise f using NAND gates only. \hfill 10 (ii) The transistor in the following circuit has \beta = 100 and V_A = 90\text{ V}. What value of R_B will give 0 volt d.c. output \hfill 10
Illustrate the Geiger-Nuttall law in a plot between the decay constant and energy of various nuclides for any radioactive series.
In the following reactions indicate with an explanation, whether they proceed by strong, electromagnetic or weak interaction or they are forbidden : \pi^+ \rightarrow \mu^+ + u_\mu p \rightarrow n + e^+ + u_e p + \pi^- \rightarrow K^+ + \Sigma^-