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.