a) Explain the wave nature of particles. Derive the time-independent Schrödinger equation for a particle in one-dimensional potential box and write its wavefunction. (Unit 1)

b) A particle of mass $9.11 \times 10^{-31}$ kg is moving in a one-dimensional box of width 10 nm. Calculate the energy of the particle in the first three excited state. (Unit 1)

a) Describe how Newton's ring experiment can be used to determine the refractive index of a liquid. (Unit 2)

b) Explain briefly the Rayleigh criterion of resolution. Discuss the resolving power of plane transmission grating and find the relation between resolving and dispersive power of the grating. (Unit 2)

a) Explain Hall effect and derive expression for Hall voltage. Discuss its application. (Unit 3)

b) Explain Fermi level for intrinsic and extrinsic semiconductors. Discuss the density of states and Bloch's theorem. (Unit 3)

a) Derive the relation between Einstein's coefficients (A & B) and explain the concept of population inversion. (Unit 4)

b) Explain the construction and working of He-Ne laser with suitable diagram. (Unit 4)

a) Prove the Poynting theorem in electrodynamics and explain the physical significance of each of the term appearing in the final expression of the theorem. (Unit 5)

b) Derive Maxwell's equations in vacuum. (Unit 5)

a) Discuss the uncertainty principle. Derive the relation between group velocity and phase velocity for a free particle. (Unit 1)

b) Calculate the NA, Acceptance angle, Critical angle and acceptance cone, for a fiber have RI of 1.55 and 1.50 respectively for its core & cladding. (Unit 4)

a) Explain acceptance angle and acceptance cone of optical fiber. Derive expression for them. (Unit 4)

b) Discuss the phenomenon of Fraunhofer diffraction at a single slit. Show that the intensity of first subsidiary maximum is about 4.5% of the principal maximum. (Unit 2)

a) Newton's rings are observed normally incident in reflected light of wavelength 6000 Å. The diameter of the $10^{\text{th}}$ dark ring is 0.50 cm, find the radius of curvature of lens and thickness of the film. (Unit 2)

b) Explain Michelson interferometer and derive expression for fringe shift due to displacement of mirror. (Unit 2)