In double-slit Fraunhofer diffraction calculate the fringe spacing on a screen 50 cm away from the slits, if they are illuminated with blue light (\lambda = 4800\text{ \AA}), slit separation d=0.10 mm, and slit-width a=0.020 mm. What is the linear distance from the central maximum the First minimum of the fringe-envelope?
Distinguish between spatial and temporal coherence.
Write a short note on Phase and Group velocities.
Write a short note on Holography.
A beam of linearly polarised light is changed into circularly polarised light by passing it through a slice crystal 0.003\text{ cm} thick. Calculate the difference in refractive index of two rays in crystal assuming this to be minimum thickness that will produce the effect and that the wavelength of light is 6 \times 10^{-7}\text{ m}.
The above expression shows that, for given W, \theta and \lambda, the resolving power is independent of number of grooves on the grating. Why do most diffraction gratings have several hundred grooves per mm?
Show that the resolving power of a diffraction grating used with light of wavelength \lambda at normal incidence is W \sin \theta/\lambda, where W is the total width of the grating \theta the angle of diffraction.
The diameter of the central zone of a zone-plate is 2.3\text{ mm}. If a point source of light (\lambda=589.3\text{ nanometer}) is placed at a distance of 6\text{ metre} from it, calculate the position of the first image.
Write a short note on Spatial and temporal coherence.
A thick wire of mass per unit length m, density p, and Young’s Modulus E, is stretched between two supports and has a tension T. Obtain from first principles an expression for the velocity of longitudinal waves in the wire. Write down the equivalent expression for velocity of transverse waves in the same wire.
Calculate the rate of energy dissipation by a damped harmonic oscillator, in the weak damping limit with \omega_o \tau \gg 1, so that \omega=\omega_o. Symbols have their usual meanings.
If two pipes one closed at one end and the other open at both ends, have fast overtones of the same frequency, what is the ratio of their respective lengths?
Two express trains travelling at 10\text{ km/hour} are meeting each other while one of them is whistling. If the frequency of the note is 800\text{ Hz}, find the apparent pitch as heard by an observer in the other train after they passed each other. Velocity of sound in air = 340\text{ ms}^{-1}.
State Huygen's principle and on its basis establish Snell's law of refraction of light. How does the result differ from what Newton's Corpuscular theory gave?
Monochromatic light of wavelength 6.56 \times 10^{-7}\text{ m} falls normally on a grating 2.00\text{ cm} wide. The first order spectrum is produced at an angle of 18^\circ15' from the normal. Deduce the total number of lines in the grating.
A beam of light of wavelength 5.82 \times 10^{-7}\text{ m} falls normally on a glass wexge with the wedge angle of 20''. If the refractive index of glass is 1.5, find the number of dark interference fringes per centimetre of the wedge length.
Fourier analyse the step-function f(x) = 1 \text{ for } 0 < x < \pi = -1 \text{ for } \pi < x < 2\pi and hence prove that 1 + \frac{1}{9} + \frac{1}{25} + \frac{1}{49} + \dots = \frac{\pi^2}{8}
The equation for displacement of point on a damped oscillator is given by x - 5e^{-0.2t} \sin \frac{\pi}{2}t \text{ metre} Find the velocity of the oscillating point at t = \frac{T}{4} and T_p where T is the time-period of the oscillator.
The speeds v of waves on the surface of a liquid is given by v = \sqrt{\frac{TK}{P} + \frac{g}{k}} where T is the surface tension of the liquid of density P > K = 2\pi / \lambda, \lambda being the wavelength of the wave and g is acceleration due to gravity Find the wavelength and frequency of waves on water which move with minimum speed.
Write a note on Oscillations with two degrees of freedom.
