Sodium light is incident normally upon a plane transmission grating having 5000 lines/cm. Calculate the angular separation of the D_1 and D_2 lines in the first order spectrum. As this angular separation is very sexy small, how can one magnify it 10 times ? (Given : \lambda_{v1} = 5690\text{ \AA} and \lambda_{v2} = 5896\text{ \AA})
Differentiate between Fresnel and Fraunhoffer diffractions. How can one explain the Fresnel diffraction pattern due to a straight edge?
What are the essential conditions for observing the interference of light? Two coherent sources with intensity ratio 4 : 1 interfere. Find I_{\text{max}} / I_{\text{min}}.
Give Rayleigh's criterion for resolution. Why telescopes with larger objectives are better? The objective of the telescope at St. Palomer has a diameter of 5.08 m. What is the least distance on Moon which could be resolved by it? (Given distance of moon from the Earth = 3,84,000 km and \lambda = 5890\text{ \AA}).
Calculate the peak values of \vec{E} and \vec{B} for a laser beam of power 2 \times 10^{10}\text{ W} and radius 0.1 mm.
Why an extended source is necessary to see colours in a soap-film ? Non-reflecting surfaces are made by coating very thin films of a transparent material. Find the maximum thickness of such thin coatings given that \lambda = 5.5 \times 10^{-5}\text{ cm} and \mu = 5/4.
Define dispersive and resolving powers of a plane transmission grating and obtain expressions for the two. Show that the first and second order spectra produced by such a grating will never overlap when the incident light contains wave-lengths in the range 4000\text{\AA} to 7000\text{\AA}.
Consider a resonant cavity of volume V of a container to which a neck of area of cross section a and length l is attached. Show that the product of the square of resonance frequency n and volume V is constant. Comment on the correction needed to the derived relation between n^2 and V. How will you determine this correction?
Write a short note on Coupled oscillations.
Calculate the minimum plate separation in a Fabry-Perot interferometer to obtain free spectral range of 0.05\text{\AA} in the wave length region 5000\text{\AA}. Calculate also the smallest resolvable wavelength difference for reflectivity of 0.95.
Stale Huygens principle and use it to establish Snell's law of refraction of light. How does this treatment of refraction differ from that given on the basis of Newton's corpuscular theory?
Write a short note on Ruby laser.
A thin quartz plate for incident light of \lambda = 6100\ \text{\AA} produces, a phase difference (45/4)\lambda between the ordinary and extraordinary rays. What will be the nature of polarisation of the emergent light when plane polarized light of wavelength 4500\text{\AA} is incident on it.
Distinguish between spatial and temporal coherence of light. What kind of coherence is required for interference and diffraction? Explain why it is possible to produce interference effects using two tuning forks of the same frequency but not by two independent sources of light of the same wavelength.
Write a short note on Ultrasonic.
Explain the terms resolving power and magnifying power of an optical instrument. On what parameter do these physical quantities depend in case of a telescope? For a given re-solving power what is the optimum magnifying power in this case ?
In a hydrogen atom for the 2\text{p} \to 1\text{ s} transition the probability per unit time is 6 \times 10^8\text{ s}^{-1}. Calculate the angular frequency of the emitted photons and the order of Einstein's coefficient \text{B}_{21}.
Why does a soap film appear coloured when is viewed by reflected white light? A thin film is illuminated by sodium light of wavelength 5900\text{\AA}. Its refractive index is 1.42. Calculate its minimum thickness so that it appears dark in reflected light.
Give the concept of Fresnel's half period zones. Describe the salient features of Fresnel's diffraction pattern due to a straight edge, showing the intensity distribution. How are these features explained?
A plane transmission grating has 6000 lines per cm. Determine the angular separation between the two lines of sodium of wavelengths 5896\text{ \AA} and 5890\text{ \AA} in the second order spectrum. If the width of the grating is 2.5\text{ cm}, will these lines be resolved?