In relation to a plane diffraction grating having 5000 lines per cm and irradiated by light of wavelength 6000\,\mathring{\mathrm{A}}, answer the following:
(i) What is the highest order spectrum which may be observed?
(ii) If the width of opaque space is exactly twice that of the transparent space, which order of spectra will be absent?
When a thin film of a transparent material is put behind one of the slits in Young's double-slit interference experiment, the zero-order fringe moves to the position previously occupied by the fourth-order bright fringe. The index of refraction of the film is n=1.2 and the wavelength of light, \lambda=5000\,\mathring{\mathrm{A}}. Determine the thickness of the film.
Write down the one-dimensional harmonic oscillator differential equation under damping and its solution for the lightly damped condition, with the meanings of symbols. Determine the dependent energy in the lightly damped condition.
A plane wave has the following expression for its electric field: \vec{E}=\hat{x}E_{0x}\cos(\omega t-kz+\alpha)+\hat{y}E_{0y}\cos(\omega t-kz+\beta) If the phase difference is defined as \delta=\beta-\alpha, under what conditions do we achieve elliptic polarization? What are the conditions for circular polarization?
Prove that the group velocity V_g of electromagnetic waves in a dispersive medium with refractive index n(\lambda_0) at wavelength \lambda_0 is given by V_g=\frac{c}{n(\lambda_0)-\lambda_0\dfrac{dn(\lambda_0)}{d\lambda_0}} where c is the free space velocity of light. Find the time taken for the electromagnetic pulse to travel a distance D.
Show that two convex lenses of the same material kept separated by a distance a, which is equal to the average of two focal lengths, may be used as an achromat, that is, a=\frac{1}{2}(f_1+f_2).
Two thin symmetrical lenses of two different natures (convex and concave) and of different materials have equal radii of curvature R=15\,\mathrm{cm}. The lenses are put close together and immersed in water \mu_w=4/3. The focal length of the system in water is 30\,\mathrm{cm}. Show that the difference between the refractive indices of two lenses is 1/3.
A laser beam of 1 micrometer wavelength with 3 megawatts power of beam diameter 10\ \mathrm{mm} is focussed by a lens of focal length 50\ \mathrm{mm}. Evaluate the electric field associated with the light beam at the focal point. (Dielectric permittivity of free space, \varepsilon_0=8\cdot8542\times10^{-12}\ \mathrm{C^2/N-m^2})
Describe Michelson interferometer for evaluation of coherence length of an optical beam. Calculate coherence length of a light beam of wavelength 600\,\mathrm{nm} with spectral width of 0.01\,\mathrm{nm}.
An unpolarized light beam of intensity 1000\ \mathrm{W/m^2} is incident on an ideal linear polarizer with its transmission axis parallel to vertical direction. Describe an experiment to reduce the intensity of light beam to 500\ \mathrm{W/m^2}.
An optical beam of spectral width 7.5\,\mathrm{GHz} at wavelength \lambda = 600\,\mathrm{nm} is incident normally on Fabry-Perot etalon of thickness 100\,\mathrm{mm}. Taking refractive index unity, find the number of axial modes which can be supported by the etalon.
Obtain the expression for the primary focal length of Fresnel zone plate.
In the propagation of longitudinal waves in a fluid contained in an infinitely long tube of cross-section A, show that \rho=\rho_0\left(1-\frac{\partial\xi}{\partial x}\right) where, \rho_0 = equilibrium density \rho = density of the fluid in the disturbed state \frac{\partial\xi}{\partial x}=\text{volume strain}\quad\left(\left|\frac{\partial\xi}{\partial x}\right|\ll1\right)
Show that two light beams polarized in perpendicular directions will not interfere.
What should be the refractive index of cladding of an optical fibre with numerical aperture 0.5 with refractive index of core as 1.5?
Distinguish between high dispersive power and high resolving power.
Obtain an expression for the resolving power of a plane transmission grating. Deduce the missing orders for a double-slit Fraunhofer pattern, if the slit widths are 0\cdot 16\text{ mm} and 0\cdot 8\text{ mm} apart.
Derive the condition for achromatism of two thin lenses separated by a finite distance and made up of same material.
Let E_A = E_1 \sin \omega t \quad \text{and} \quad E_B = E_2 \sin (\omega t + \delta) By using analytical method, obtain an expression to explain interference. Also show that intensity varies along the screen in accordance with the law of cosine square in interference pattern.
Explain the phenomenon of interference in thin films. Why is the contrast better in brightness of fringes obtained from the interference of reflected light rays compared to the transmitted light rays?