Explain mathematically how left and right circularly polarized light is produced by combining two linearly polarized beams. Given a beam of light, how can one experimentally test whether it is unpolarized or circularly polarized?
What is hologram? Explain how the image of the object is formed when one looks through it.
Write a note on Rayleighs criterion and resolving power of a telescope.
Show schematically the intensity distribution for a 2-slit Fraunhofer diffraction-interference, if slit-widths are 2\lambda each and centres of slits have separation 6\lambda. Assume incident light falling normally, and limit the discussion to the central diffraction band range.
A single, slit of width 0.14\text{ mm} is illuminated normally by monochromatic light and diffraction bands are observed on a screen 2\text{ m} away. If the centre of the second dark band is 1.6\text{ cm} from the middle of the central bright band deduce the wavelength of light.
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?
Explain the Laser actions in
(i) Helium Neon Laser
(ii) Gas Laser
A beam of lineal polarised light is changed into circularly polarised light by passing it through a slice of double-refracting crystal 0.0030 cm thick. Calculate to difference in the two refractive indices of the crystal, assuming this to be minimum thickness that will produce the result, and that the wavelength is 6 \times 10^{-5}\text{ cm}.
Write a short note on Fraunhofer diffraction by circular aperture.
Write a short note on Rayleigh criterion for resolution.
Distinguish between spatial and temporal coherence.
Write a short note on Phase and Group velocities.
For transverse waves passing over a uniform string, prove that the slope of the siring at any position x at a given time is numerically equal to the ratio of the particle speed at that position x and time to the wave speed over the string.
How can it be proved experimentally that energy transmission is associated with a wave? The disc of a siren having 60 holes makes 420 revolutions per minute. Find the wavelength of its sound in air 0^\circ\text{C}, if velocity of sound at 0^\circ\text{C} is 332\text{ ms}^{-1}.
A movable bridge divides sonometer wire into two parts, which differ in length by 1.0 cm and produce 4 beats pre second when sounded together. If the whole length of the wire is 100 cm, find the frequencies of the parts.
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.
Write a short note on Holography.
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}.
