Question 1

Necessary conditions for interference.

Accepted Answer

In reflected light, the interference minima have nearly zero intensity resulting in high contrast, while in transmitted light, the interfering waves have vastly different amplitudes leading to poor contrast.

Question 2

Relation between phase difference and path difference.

Accepted Answer

De Broglie wavelength is the wavelength associated with a moving material particle, given by $\lambda = \frac{h}{p}$.

Question 3

Population inversion.

Accepted Answer

Spatial coherence refers to phase correlation across different points in space, while temporal coherence refers to phase correlation over a period of time at a single point.

Question 4

Stimulated emission.

Accepted Answer

The unit of Einstein's A coefficient is $s^{-1}$ and the B coefficient is $m^3 J^{-1} s^{-2}$.

Question 5

Heisenberg Uncertainty Principle.

Accepted Answer

The Fermi-Dirac distribution function gives the probability that a given available electron energy state will be occupied at a given temperature.

Question 6

Group velocity and Phase velocity.

Accepted Answer

Two key properties are high electrical/thermal conductivity and malleability/ductility.

Question 7

Lorentz force.

Accepted Answer

The curl of a magnetic field represents the source of the magnetic circulation, which is the total electric current density passing through a point.

Question 8

Continuity equation for charge.

Accepted Answer

The Biot-Savart law in vector form relates the infinitesimal magnetic field $d\vec{B}$ to the infinitesimal current element $I d\vec{l}$.

Question 9

Intrinsic and Extrinsic semiconductors.

Accepted Answer

Bragg's law gives the condition for constructive interference of X-rays scattered by parallel crystal planes: $2d \sin 	heta = n\lambda$.

Question 10

Meissner effect in superconductors.

Accepted Answer

For wavefronts overlapping with a degree of partial coherence of 0.40, assuming equal beam intensities, the fringe visibility is 0.40.

Question 11

Newton's rings: diameter of nth and (n+p)th rings, find $\lambda$.

Accepted Answer

When a transparent glass plate of thickness $t$ and refractive index $\mu$ is introduced into one arm of a Michelson Interferometer, it increases the optical path length by $(\mu - 1)t$. This causes the entire fringe pattern to shift. The number of shifted fringes $n$ is given by $n = \frac{(\mu-1)t}{\lambda}$.

Question 12

Dispersive power of grating.

Accepted Answer

In quantum mechanics, the wave function $\psi$ itself has absolutely no direct physical meaning. However, Max Born's interpretation dictates that the absolute square of the wave function, $|\psi|^2 = \psi^*\psi$, represents the physically meaningful Probability Density of finding the particle at a specific location in space.

Question 13

Einstein's coefficients A and B relation.

Accepted Answer

The fundamental requirements for laser action are an Active Medium capable of stimulated emission, an external Pumping Source to provide energy, a Metastable State to temporarily trap atoms, and an Optical Resonator cavity to provide positive feedback and massive amplification of the coherent light.

Question 14

Compton effect: change in wavelength.

Accepted Answer

The Hall coefficient ($R_H$) is a fundamental material property defined as $R_H = \frac{1}{nq}$, relating the induced transverse Hall electric field to the product of current density and magnetic field. It is crucial for determining whether a semiconductor is p-type or n-type, and for calculating exact carrier concentrations.

Question 15

Displacement current.

Accepted Answer

The Poynting vector, denoted as $\vec{S}$, is the cross product of the electric and magnetic fields ($\vec{S} = \vec{E} 	imes \vec{H}$). It represents the directional rate of energy transfer (power flux density) carried by an electromagnetic wave per unit area.

Question 16

Numerical: Fiber with core $\mu_1 = 1.5$ and cladding $\mu_2 = 1.45$, find $N…

Accepted Answer

By applying the Newton's rings formula $\lambda = D_n^2 / (4nR)$, with the 10th dark ring diameter of $0.5	ext{ cm}$ and a lens radius of curvature of $100	ext{ cm}$, the wavelength of the monochromatic light is meticulously calculated to be exactly $6250	ext{ \AA}$.

Question 17

Type I and Type II superconductors.

Accepted Answer

Using the quantum mechanical "particle in a box" model, the zero-point ground state energy ($n=1$) for an electron confined strictly within an infinitely deep one-dimensional potential well of width $1	ext{ \AA}$ is precisely calculated to be approximately $37.7	ext{ eV}$.

Question 18

Michelson Interferometer: construction and working.

Accepted Answer

Fraunhofer diffraction at a single narrow slit is analyzed by dividing the wavefront into infinitesimally small elements and applying Huygens' principle. The mathematical integration of these secondary wavelets across the slit width perfectly derives the distinctive diffraction pattern characterized by a massive central maximum and rapidly fading secondary intensity bands.

Question 19

Davisson-Germer experiment.

Accepted Answer

The Time-Independent Schrödinger Equation is rigorously derived by separating the time and space variables of the full time-dependent wave equation. By applying classical energy relations and de Broglie's wave hypothesis, it mathematically isolates the stationary energy states of quantum systems.

Question 20

Ruby laser construction and working.

Accepted Answer

The He-Ne laser is a continuously operating gas laser that utilizes an electrical discharge to excite a helium-neon gas mixture. Helium atoms act as a highly efficient pumping mechanism, transferring their energy to neon atoms via resonant collisions to establish the critical population inversion necessary for laser action.

Question 21

Hall effect: derivation of $R_H$.

Accepted Answer

Light propagates through optical fibers via Total Internal Reflection. The Acceptance Angle represents the maximum cone of light a fiber can capture. For a fiber with NA=0.20 submerged in water, the acceptance angle is calculated to be highly constrained at $8.65^{\circ}$.

Question 22

Plane EM waves in vacuum: velocity $c = 1/\sqrt{\mu_0 \epsilon_0}$.

Accepted Answer

Maxwell's four differential and integral equations represent the ultimate unification of electricity and magnetism. They govern how electric charges generate electric fields (Gauss's Law), prohibit magnetic monopoles, describe electromagnetic induction (Faraday's Law), and prove that changing electric fields generate magnetic fields (Ampere-Maxwell Law).

Engineering Physics