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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.
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).
Consider a system of two thin lenses of focal lengths +15\text{ cm} and -20\text{ cm} separated by a distance of 25\text{ cm} in air. Determine the system matrix. For an object of height 1\text{ cm} placed at a distance of 27\cdot 5\text{ cm} in front of the convex lens, find the size and position of the image.
(i) What is birefringence? Indicate how it can be used to obtain plane and circularly polarized light.
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?
(i) Between multimode and single-mode fibers, explain critically how and why single-mode fiber is chosen for communication.
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})
For stationary waves on a string whose ends are fixed, show that the energy density is maximum at antinodes and minimum at nodes.
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?
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.
What are the important properties of a hologram?
Optical power of 1\text{ mW} is launched into an optical fiber of length 100\text{ m}. If the power emerging from the other end is 0\cdot 3\text{ mW}, calculate the fiber attenuation.
A plane-polarised light is incident perpendicularly on a quartz plate cut with faces parallel to optic axis. Find the thickness of the quartz plate which introduces phase difference of 60^\circ between e- and o-rays.
At what temperature are the rates of spontaneous and stimulated emission equal? (Assume \lambda = 500\text{ nm})
Show that the plane of polarisation is rotated through \theta = \frac{\delta}{2} = \frac{\pi d}{\lambda} (\mu_L - \mu_R) in optical rotation where symbols have their usual meanings.
Derive the condition for achromatism of two thin lenses separated by a finite distance and made up of same material.
What are the characteristics of stimulated emission? Show that in the optical region, stimulated emission is negligible compared to spontaneous emission.
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.
Explain how inversion of population is achieved in a He-Ne laser.