A diffraction grating has 5000\text{ lines per cm}. For illumination at normal incidence, determine the dispersive power of the grating in the second order spectrum in the range of wavelengths around 500\text{ nm}.

With a suitable diagram, deduce an expression for numerical aperture (NA) for an optical fiber having refractive indices of core and cladding n_1 and n_2, respectively and being placed in a medium of index n_0.

A slit 0\cdot 25\text{ mm} wide is placed in front of a convex lens and illuminated by plane waves of wavelength 500\text{ nm}. The Fraunhofer diffraction pattern is formed in the focal plane of the lens. In the pattern, the distance from the third minimum on the left to the third minimum on the right is found to be 3\text{ mm}. Find the focal length of the lens.

What do you mean by underfilled and overfilled conditions with reference to numerical aperture in exciting light in fiber?

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.

(ii) Determine its quality factor Q and width of resonance \Delta f.

Why is the NA of the single-mode optical fiber low as compared to multimode fiber?

(i) Between multimode and single-mode fibers, explain critically how and why single-mode fiber is chosen for communication.

(ii) Why are the two wavelengths 1\cdot 30\ \mu\text{m} and 1\cdot 55\ \mu\text{m} important in single-mode fiber-optical communication system?

(i) What is birefringence? Indicate how it can be used to obtain plane and circularly polarized light.

(ii) A left circularly polarized beam of light having \lambda_0 = 5893\text{ \AA} is incident on a calcite crystal with its optic axis cut parallel to the surface. The crystal has thickness d = 0\cdot 005141\text{ mm}, n_o = 1\cdot 65836 and n_e = 1\cdot 48641 at this \lambda_0. What will be the state of polarization of the incident beam?

Consider a bare fiber having n_1 = 1\cdot 48 and n_2 = 1\text{ (air)}. Find out the NA. What is the maximum incident angle up to which light can be guided through the fiber?