Numericals

1. The speed of light in an unknown medium is measured to be 2.76 x 10⁸ m/s.  (a)  What is the index of refraction of the medium? (ans: 1.09.)


2. Optical fibers are generally composed of silica, with an index of refraction around 1.44.  (a)  How fast does light travel in a silica fiber, and (b)  How long will it take for that light to travel from St. Petersburg, Florida to Anchorage, Alaska? (given: distance between these two cities is 6091 km)

Solution:

 

(a)	The speed of light in this fiber is found to be v = c/n = (3.00 x 108 m/s)/(1.44) = 2.08 x 108 m/s.
(b)	The distance between these two cities is 6091 km, or 6.091 x 106 m.  Since speed is distance x over time t, we find t = x/v = (6.091 x 106 m)/(2.08 x 108 m/s) = 2.92 x 10-2 s, or 29.2 ms.

Refraction is simply mean a change in path of light in given media

The phenomenon of change in path of light in going from one medium to another is called refraction of light. Thus the refraction of light is the phenomenon of bending of light from its original path  on entering another medium. the refraction occurs right at the boundary of the two media

Snell's Law

Snell's Law relates the indices of refraction n of the two media to the directions of propagation in terms of the angles to the normal. Snell's law can be derived from Fermat's Principle or from the Fresnel Equations.