An optical fiber has index of refraction `n=1.40` and diameter `d=100 mu m`. It is surrounded by air. Light is sent into the fiber along the axis as shown in figure. If smallest outside raidus R permitted for a bend in the fiber for no light to escape is given by 50 x (in `mu` m) fill value of x.

A cylinderical optical fibre (quarter circular shape) of refractive index n = 2 and diameter d = 4mm is surrounded by air. A light beam is sent into the fibre along its axis as shown in figure. Then the smallest outer radius R (as shown in figure) for which no light escapes after incident on curved surface of fibre is: .

An optical fibre has diameter d and is made of material of refractive indeed mu . It is surrounded by air. Light is made to enter through one end of the fibre as shown. The fiber is in the shape of a circular bend of outer radius r. (a) Find least value of r (= r_(o)) for which no light can escape out of the fibre. Calculate r_(o) for d = 200 mum and mu = 1.4 . (b) How is value of r_(o) affected as d is made smaller? (c) For sharper bends, shall we have higher mu or smaller mu ?

In figure, the optical fiber is l = 2 m long and has a diameter of d = 20 mum. If a ray of light is incident on one end of the fiber at angle theta_1=40^@ , the number of reflections it makes before emerging form the other end is close to : (refractive index of fiber is 1.31 and sin40^@=0.64 )

A portion of a straight glass rod of diameter 2 cm and refractive index 1.5 is bent into an arc of a circle of radius R cm and a parallel beam of light is incident on it as shown in figure. Find the smallest R which permits all the light to pass around the arc.

A ray of light strikes an air-glass interface such that a part of it is reflected into air and the rest enters glass as shown in the figure below. If angle of refraction and refractive index of glass with respect to air is r and mu respectively,then value of alpha is

What is the least radius through which an optical fiber of core diameter 0.05 mm may be bent (as shown in figure) without serious loss of light? The refractive index of the core is 1.6 and that of cladding is 1.5.

A light source S is placed at the centre of a glass sphere of radius R and refractive index mu . The maximum angle theta with the x-axis (as shown in the figure) an incident light ray can make without suffering total internal reflection is

A transparent thin film of uniform thickness and refractive index n_(1) =1.4 is coated on the convex spherical surface of radius R at one end of a long solid glass cylinder of refractive index n_(2) =1.5 , as shown in the figure. Rays of light parallel to the axis of the cylinder traversing through the film from air to glass get focused at distance f_(1) from the film, while rays of light traversing from glass to air get focused at distance f_(2) from the film, Then