Refractive Index

Refractive Index and Speed of Light
The refractive index, n, of a medium may also be defined as the ratio of the speed of light in a vacuum ( C) to the speed of light in that medium (Cn).
Namely, n = C/Cn

Question
If the speed of light in air is 3.00.000.000 m/sec, find the speed of light in diamond. (Refractive index of diamond = 2,42)

Solution
n       = C/Cn
2,42 = 3,/Cn
Cn   = 3.00.000.000/2,42
       = 124.000.000 m/sec

Note: The higher the refractive index of a medium, the slower will be the speed of light through it. This means that medium’s optical density increase as its refractive index increase.

Refractive Index and Wavelength of Light
The refractive index, n, of a medium may also be defined as the ratio of the wavelength of light in a vacuum (lambda) to the Wavelength of light in that medium
(lamda n). Namely, n = lambda/ lambda n
Question
Monochromatic red light of wavelength 640 nm (nanometer) passes from air into
glass plate of refractive index 1,5. What is the wavelength of this light inside the
glass?
Plan: The wavelength will be less in the glass due to the slower speed of the light.
Solution:
ng = la/ lg
lg = la/ ng
lg = 640/1, 5
= 427 nm
Exercises
1. Sketch rays diagram below!

2. The speed of light in vacuum is 3.00.000.000 m/s. What is the speed of light in a medium whose refractive 

     index  is  1,42?

3. Monochromatic yellow light of wavelength 880 nm passes from air into water. If the wavelength of this 

    light  in water 660 nm, what is the refractive index in water?