Sample Problems for The Index of Refraction

Sample Problems for The Index of Refraction

Important Information

Your reading introduced you to the concept of index of refraction, n, defined by

n = c/v, where
c = 2.99792458 x 10⁸m/s.

v in this equation is the speed of light in a medium having an index n, and c represents the speed of light in vacuum.

Sample Problem 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? (b) Does it match any of the materials listed in your Table?

Solution:

(a)	The index is found to be n = c/v = (3.00 x 108 m/s)/(2.76 x 108 m/s) = 1.09.
(b)	This does not equal any of the indices of refraction listed in the table. It is closest to air, which suggests it is some slightly denser gas.

Sample Problem 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?

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)	According to AskJeeves, 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.

Practice Exercises

On-Line Reading

At-Home Assignments

Click on the Next or Prev button to go to sample problems for other topics.