What is axial chromatic aberration? A convex lens has a focal length of 15.5 \times 10^{-2}\,\mathrm{m} for red colour and 14.45 \times 10^{-2}\,\mathrm{m} for violet colour. If an object is kept at a distance of 40\,\mathrm{cm} from the lens, calculate the longitudinal chromatic aberration of the lens.
Prove that when light goes from one point to another via a plane mirror, the path followed by light is the one for which the time of flight is the least.
When the two waves of nearly equal frequencies interfere, then show that the number of beats produced per second is equal to the difference of their frequencies.
What do you mean by spherical aberration of a lens? Show that if two plano-convex lenses are kept at a distance equal to the difference of their focal lengths, the spherical aberration would be minimum.
Discuss the intensity distribution in Fraunhofer diffraction pattern due to a single slit. Obtain conditions for maxima and minima of the intensity distribution. Show that the intensity of the first maxima is about 4.95\% of that of the principal maxima.
A plane transmission grating has 3000 lines in all, having width of 3\ \mathrm{mm}. What would be the angular separation in the first order spectrum of the two sodium lines of wavelengths 5890\mathring{\mathrm{A}} and 5896\mathring{\mathrm{A}}? Can they be seen distinctly?
Explain the principle and working of He-Ne laser. What is the role of He gas? Why is it necessary to use narrow tube? How many longitudinal modes can be excited for an He-Ne laser in a cavity of length 30 cm and having half width of gain profile of laser material 2 \times 10^{-3}\,\mathrm{nm}? The emission wavelength is 6328\,\mathring{\mathrm{A}}.
Distinguish between positive and negative crystals in terms of double refraction. How are these crystals used to make quarter wave plates? Explain how the quarter wave plate is used in producing elliptically and circularly polarized light.
Explain the principle of operation of optical fibre. What are the different losses that take place in optical fibre?
What is multiple-beam interference? Discuss the advantages of multiple-beam interferometry over two-beam interferometry. Explain the fringes formed by Fabry-Perot interferometer.
Show that the areas of all the half-period zones are nearly the same. Find the radius of 1st half-period zone in a zone plate whose focal length is 50\ \mathrm{cm} and the wavelength of the incident light is 500\ \mathrm{nm}.
Sunlight is reflected from a calm lake. The reflected light is 100% polarized at a certain instant. What is the angle between the sun and horizon?
Obtain the system matrix for a thin lens placed in air and made of material of refractive index 1.5 having radius of curvature 50\,\mathrm{cm} each. Also find its focal length.
A plane-polarized light passes through a double-refracting crystal of thickness 40\,\mu\mathrm{m} and emerges out as circularly polarized. If the birefringence of the crystal is 0.00004, then find the wavelength of the incident light.
Explain with proper example the interferences due to 'division of wavefront' and 'division of amplitude'.
How is laser light different from ordinary light? Discuss the working principle of ruby laser. What role do chromium ions play in this process?
Find the velocity of sound in a gas in which two waves of wavelengths 1.00\,\mathrm{m} and 1.01\,\mathrm{m} produce 10 beats in 3 seconds.
The refractive indices of core and cladding in a step index optical fiber are 1.52 and 1.48 respectively. The diameter of the core is 30\,\mu\mathrm{m}. If the operating wavelength is 1.3\,\mu\mathrm{m}, calculate the V parameter and the maximum number of modes supported by the fiber.
Explain the principle of (i) induced absorption, (ii) spontaneous emission and (iii) stimulated emission. Show that the ratio of Einstein's coefficients is given by \frac{A}{B}=\frac{8\pi h\nu^{3}}{c^{3}}
Obtain an expression for the resolving power of a grating explaining the Rayleigh's criterion of resolution.
