# Physics 2006-07

Notes : (i) Attempt all questions.

(ii) Marks carried by the questions are shown against it.

(Hi) The physical constants are given at the end of the question paper.

1. Attempt any four of the following :

(a) Using the postulates of special theory of relativity, deduce the Lorentz transformation equations.

(b) Calculate the percentage contraction in the length of rod in a frame of reference, moving with velocity 0.8 c in a direction at an angle of 30° with its length.

(c)   A stone is dropped from an aeroplane moving with a constant horizontal velocity. What will be the path (i) as observed by the pilot (ii) as observed by a man standing on the earth ? If both are different then explain why ?

(d) If frame S’ is moving with velocity vi with respect to frame S, and the component of velocity in frame S’ are u’x = c cos(|) and u’y = c sin(|) then prove that for the frame 2S, ux+uy =c .

(e) A spaceship moving away from the earth with velocity 0.5 c fires a rocket whose velocity relative to the space is 0.5 c. Calculate the velocity of the rocket as observed from the earth in following two cases :

(i) away from the earth

(ii) towards the earth

(f)  Is there any condition at which the Lorentz transformation reduces to Galilian transformation ? Explain it by taking suitable example.

2. Attempt any four of the following :

(a) In a biprism experiment the micrometer reading for zero order and tenth order fringes are 1.25 mm and 2.37 mm respectively when light of X = 5.90 x 10-5 cm. is used. Now what will be the position of zero order and tenth order fringes if X is changed to 7.50 x 10-5 cm.

(b) Find the expression for the fringe width in case of wedged-straped thin film.

(c) Explain what happens when :

(i)  Glass plate is replaced by plane mirror in Newton’s ring experiment

(ii) Thickness of wedged-straped thin film becomes very large.

(iii) A sheet of mica is introduced in the path of one of the interfering wave in Fresnel’s biprism experiment.

(d) What is advantage of oil immersion objective in microscope ? Derive the expression for the resolving power of microscope.

(e) A diffraction grating is just able to resolve two lines ofX = 5140.34 A° and 5140.85 A° in the first order. Will it resolve the lines 8037.20 A° and 8037.50 A° in the second order ?

(f) (i) What are the difference between interference and diffraction ?

(ii) A light of wavelength 5500 A° falls normally on a slit of width22.0x 10-5 cm. Calculate the angular position of the first two minima on either side of the central maxima.

3. Attempt any four of the following :

(a) What is quarter wave plate ? Describe its method of construction and use. Deduce its thickness for a given wavelength in terms of refractive indices.

(b) Plane polarized light is incident on a plate of quartz cut with faces parallel to optic axis calculate :

(i)  the ratio of intensities of extraordinary and ordinary light if the vibrations in the incident light make an angle of 30° with the crystal.

(ii) the least thickness of the plate for which extraordinary and ordinary beams on emergence recombine to form plane polarised light. (Given X = 6000 A°,= 1.5442, (4,^ = 1.5532)5×4

(c) Define the plane of polarization. Give Fresnel’s explanation of the rotation of polarization.

(d) (i) Define the specific rotation

(ii) On introducing a polarimeter tube of 25 cm. long containing a sugar solution of unknown strength it is found that the plane of polarization is rotated through 10°. Find the strength of the solution in gm/cm3. Given specific rotation of sugar solution 60° per decimeter per unit concentration.

(e) (i) Comment on the statement, “Polarization requires that the vibrations are transverse.”

(ii) Can sound waves be polarised ? Give reasons for your answer.

(f)  Find the ratio of population of the two states in a He-Ne laser that produces light of wavelength 6328 A0 at 27°C. (Given that k (Boltzman constant) is 8.61 x 10-5 eV/K)

4. Attempt any two of the following :

(a) (i) Explain the concept of displacement current. Write four Maxwell’s equations and explain their physical significance.

(ii) What do you mean by continuity equation and deduce an expression for this equation ?

(b) (i) The relative permittivity of distilled water is 81. Calculate refractive index and velocity of light in it.

(ii) A plane electromagnetic wave propagating along the X-direction has a wavelength 5.0 mm. The electric field is in the y -direction and its maximum magnitude is 38 V/m. Write the equation of the electric and magnetic fields as a function of x and t.

(c) (i) Prove that the energy dissipated per cc. of the magnetisation is |i0 times the area of M – H (or I-H) curve.

(ii) Calculate the hourly loss of energy in the iron core of a transformer, the hysterisis loop of which is equivalent in area to 3000 ergs/cm3. Given frequency 50 cycles/sec, density of iron 7.5 gm/cc and weight of the core 12 kg.

5. Attempt any two of the following :

(a) Discuss quantum mechanically the problem of linear harmonic oscillator and obtain its eigen values. Also write significance of zero point energy.

(b) What is Compton effect ? Derive an expression h for Compton shift, = m c ~~ cos ®) where the symbols are having their usual meanings.

(c)   (i) A set of lattice planes reflects X-rays of wavelength 1.32 A0 at a glancing angle of 9° 30′. Calculate the possible spacing of this set of planes for different order of reflections. (Given that sin 9° 30′ = 0.1650)

(ii) Compute the energy difference between the ground state and the first excited state for an electron in a one-dimensional rigid box of length 10-8 cm. Planck’s constant h = 6.63 x 10-34 J.s. Velocity of light in free space c = 3 x 108m/s Electronic charge e=1.6 xl0_19c Permittivity of free space e0= 8.85×10″ 12 F/m Permeability of free space |j,0 = 4 % x 10 “7 H/m Rest mass of electron me = 9.1 x 10-31 kg