Question

A beam of monochromatic light (f = 5.09 ×1014 Hz)

has a wavelength of 589 nanometers in air. What
is the wavelength of this light in Lucite?

Answer 1

393 nm

Step-by-step explanation:

The index of refraction of lucite is:

n = 1.50

The speed of light in lucite is given by:

`v=(c)/(n)=(3\cdot 10^8 m/s)/(1.50)=2\cdot 10^8 m/s`

where c is the speed of light in a vacuum.

The wavelength of the light in Lucite is given by

`\lambda=(v)/(f)`

where

`v=2\cdot 10^8 m/s` is the speed of light in Lucite

`f=5.09\cdot 10^(14)Hz` is the frequency

Substituting,

`\lambda=(2\cdot 10^8 m/s)/(5.09\cdot 10^(14) Hz)=3.93\cdot 10^(-7) m = 393 nm`