Obtain the relation to find radii of the rings and the wavelength of light in Newton's circular ring. Calculate the radius of curvature of the convex glass surface where diameter of 5^{th} and 15^{th} bright rings formed by sodium yellow light are measured to be 2.303\text{ mm} and 4.134\text{ mm}. Given \mu = 1.5 and \lambda_{yellow} = 5282 \text{\AA}.
Explain the working of Michelson interferometer using appropriate optical diagram. also draw paths of the rays.
The X and Y co-ordinates of Cornu's spiral can be expressed quantitatively by two integrals. Derive the expressions of these integrals.
In the steady state forced vibration a point particle of mass 'm' moves under the influence of an external force (F \sin pt) \hat{i} in addition to the restoring force - (kx) \hat{i} and damping force - (\beta x) \hat{i} . Show that (i) the amplitude is maximum when p = \sqrt{\omega^2 - 2b^2} , where k/m = \omega^2 and (ii) the value of the maximum amplitude is \frac{f}{2b \sqrt{\omega^2 - 2b^2}} . What do you mean by the sharpness of resonance ?
How would you produce plane polarized light by reflection ? What is Brewster's law ? Calculate the angular position of the sun above the horizon so that light reflected from a calm lake is completely polarized. The refractive index of water is 1.33. Circularly polarized and unpolarized light are passed in turn through a Nicol prism. The Nicol is rotated about the direction of light as axis. What would you observe in each case ? How would you distinguish between them ?
Differentiates between Rayleigh and Raman scatterings. Why is Raman scattering considered to be a breakthrough in molecular spectroscopy ? What are the advantages of using laser light in Raman spectroscopy ?
(c) Why does one see two image points for a single object point while viewed through a calcite crystal ? What is this property of the crystal known as ? What is an optic axis of a crystal ? Explain the meanings of positive and negative crystals with one example for each kind.
(b) What is the essential difference between interference and diffraction of light ? How can you achieve Fraunhofer diffraction in the laboratory ? Using the concept of Fraunhofer diffraction at a single slit, find out the intensity distribution produced by two slits of equal width.
(b) For a transverse sinusoidal wave of wavelength \lambda propagating along negative x direction through a string fixed at a point, show that the nodes are located at x = 0, \lambda/2, \lambda, 3\lambda/2, \dots while the kinetic energy / unit length at the antinodes is given by E = 2 \rho A^2 \omega^2 \cos^2 \omega t where \rho, A and \omega, are the mass density / unit length, amplitude of transverse displacement and angular frequency of the wave, respectively.
(c) What do you understand by paraxial rays ? Show that the effect of translation of a paraxial ray while travelling along a homogeneous medium is represented by a 2 \times 2 matrix if the ray is initially defined by a 2 \times 1 matrix.
(c) Explain how Einstein's A and B coefficients are related to the phenomena of spontaneous and stimulated emission of radiation, respectively. Derive the relation between A and B. Establish that at very high frequency around X-ray wavelength regime, lasers cannot be made as easily as at low frequencies, e.g. far infra-red regime.
(d) Drawing a neat diagram, discuss how light travels through an optical fibre. Show that the numerical aperture of a commercially available optical fibre is around 0.25. Explain its physical significance.
A siren of frequency 900 Hz is going towards a wall away from an observer at a speed 10 m/sec. Determine : (i) Frequency of sound directly heard from the siren. (ii) Frequency of sound reflected from the wall. (iii) Number of beats per second heard by the observer. (Velocity of sound = 330 m/sec)
A narrow slit illuminated by monochromatic light of \lambda = 6400\text{ \AA} is placed at a distance of 3 metres from a straight edge. If the distance between the straight edge and the screen is 6 metres, calculate the distance between the first and the fourth dark bands.
A quartz quarter wave plate is to be used with the sodium light (\lambda = 5896\text{ \AA}). What should be its thickness ?
Water vapor shows Infrared absorption bands at 1595\text{ cm}^{-1}, 3652\text{ cm}^{-1} and at 3756\text{ cm}^{-1}. If the Raman spectrum is observed with the Argon Ion Laser 514.5\text{ nm}, at what wavelengths would you expect to find the Raman Stokes lines ?
Differentiates between Rayleigh and Raman scatterings. Why is Raman scattering considered to be a breakthrough in molecular spectroscopy ? What are the advantages of using laser light in Raman spectroscopy ?
Two microscope slides of length 10 cm each form a wedge. At one end they are in contact and at the other end they are separated by a thin wire of diameter d (see the diagram below). Interference fringes are obtained when illuminated vertically by a monochromatic light of \lambda = 500\text{ nanometers}. The fringe spacing is found to be 1.25 cm. Estimate the diameter of the wire.
