PYQ Bank

State Biot-Savart law. Calculate the magnitude of axial magnetic induction due to a circular loop of area A carrying current I.

For an arbitrary localised charged distribution, obtain an expression of electrostatic potential V in terms of multipole expansion.

A plane-polarised electromagnetic wave is incident on the interface of two dielectrics having dielectric permittivity \varepsilon_1 and \varepsilon_2. Assume that the electric vector \vec{E} lies in the plane of incidence. Using the boundary conditions at the interface, obtain the expressions for the amplitude reflection coefficient (r_{11}) and the amplitude transmission constant (t_{11}). Using the components of the Poynting vector \vec{E} \times \vec{H} associated with the reflected and transmitted waves, obtain the expressions for reflection and transmission coefficients R_{11} and T_{11} respectively. Under what condition, r_{11} = 0 and t_{11} = 1?

Using Planck's radiation formula, deduce Wien's displacement law.

In a non-charged current-free dielectric, \rho = 0 and \vec{J} = 0. Show that in this medium, electric (\vec{E}) and magnetic (\vec{H}) fields satisfy three-dimensional wave equations \nabla^2 \vec{E} = \varepsilon\mu \frac{\partial^2 \vec{E}}{\partial t^2} \quad \text{and} \quad \nabla^2 \vec{H} = \varepsilon\mu \frac{\partial^2 \vec{H}}{\partial t^2} Using Poynting theorem of electromagnetic theory, describe the significance of the vector \vec{P} = (\vec{E} \times \vec{H}) and the scalar u = \frac{1}{2} [\vec{B} \cdot \vec{H} + \vec{D} \cdot \vec{E}]

Consider the incidence of a plane-polarised electromagnetic wave at the interface of two media having dielectric permittivity and magnetic permeability (\varepsilon_1, \mu_1) and (\varepsilon_2, \mu_2) respectively. The interface is chosen to be x = 0 plane. \vec{K}_1, \vec{K}_2 and \vec{K}_3 represent the propagator vectors associated with the incident, refracted and reflected waves respectively. Using the boundary conditions on them, establish the Snell's laws of refraction.

Obtain an expression for the resolving power of a plane transmission grating. Deduce the missing orders for a double-slit Fraunhofer pattern, if the slit widths are 0\cdot 16\text{ mm} and 0\cdot 8\text{ mm} apart.

Optical power of 1\text{ mW} is launched into an optical fiber of length 100\text{ m}. If the power emerging from the other end is 0\cdot 3\text{ mW}, calculate the fiber attenuation.

Explain the phenomenon of interference in thin films. Why is the contrast better in brightness of fringes obtained from the interference of reflected light rays compared to the transmitted light rays?

Let E_A = E_1 \sin \omega t \quad \text{and} \quad E_B = E_2 \sin (\omega t + \delta) By using analytical method, obtain an expression to explain interference. Also show that intensity varies along the screen in accordance with the law of cosine square in interference pattern.

For stationary waves on a string whose ends are fixed, show that the energy density is maximum at antinodes and minimum at nodes.

A plane-polarised light is incident perpendicularly on a quartz plate cut with faces parallel to optic axis. Find the thickness of the quartz plate which introduces phase difference of 60^\circ between e- and o-rays.

Derive the condition for achromatism of two thin lenses separated by a finite distance and made up of same material.

At what temperature are the rates of spontaneous and stimulated emission equal? (Assume \lambda = 500\text{ nm})

Distinguish between high dispersive power and high resolving power.

Show that the plane of polarisation is rotated through \theta = \frac{\delta}{2} = \frac{\pi d}{\lambda} (\mu_L - \mu_R) in optical rotation where symbols have their usual meanings.

What are the important properties of a hologram?

What are the characteristics of stimulated emission? Show that in the optical region, stimulated emission is negligible compared to spontaneous emission.

Two bodies of masses M_1 and M_2 are placed at a distance d apart. Show that at this position where the gravitational field due to them is zero, the potential is given by V = -\frac{G}{d} (M_1 + M_2 + 2\sqrt{M_1 M_2})

Obtain the relativistic equation for aberration of light using velocity transformation equations.