### Sample Problem 1: Speed and Frequency of Light Leaving an Optical Fiber

Light moving from an optical fiber to air changes wavelength from 452nm to 633nm.

A.
What is the index of refraction of the fiber?
B.
What is the speed of light in the fiber?
C.
What is the frequency of the light in the fiber?
D.
What is the frequency of the light in air?
A.
Since we do not have five digits of accuracy in this problem, we can assume that the wavelength of light in air, air = 633 nm is the wavelength of the light in vacuum 0.

The index of refraction inside the fiber is 1.40.

B.
From the definition of n, we have

The speed of light inside the fiber is 2.14 x 108m/s.

C.
The frequency in the fiber can be found from the speed and the wavelength in the fiber:

D.
The frequency of light does not change as the light moves between two different media, so the frequency in air is the same as the frequency in the fiber: 4.74 x 1014Hz. You can double-check this result by calculating the frequency from the speed of light and wavelength in air: