Question

If the wavelength of a monochromatic source is 600 nm in vacuum, what is the wavelength from the same source when it passes through a liquid where the speed of light is 2.00 ´ 108 m/s? (c = 3.00 ´ 108 m/s)

Answer 1

In vacuum, the wave has a wavelength of

`\lambda=600 nm=6\cdot 10^(-7)m`
and it travels at speed of light

`c=3 \cdot 10^8 m/s`
So its frequency is

`f= (c)/(\lambda)= (3 \cdot 10^8 m/s)/(6 \cdot 10^(-7)m)=5.0 \cdot 10^(14)Hz`

The frequency of an electromagnetic wave does not change when moving from a medium to another, and since the new speed of the wave in the liquid is

`v=2.00 \cdot 10^8 m/s`
we can find its new wavelength when moving in the liquid:

`\lambda'= (v)/(f)= (2.00 \cdot 10^8 m/s)/(5.0 \cdot 10^(14)Hz)=4.0 \cdot 10^(-7) m = 400 nm`