Question

Light in vacuum is incident on the surface of a slab of transparent material. In the vacuum the beam makes an angle of 39.9° with the normal to the surface, while in the slab it makes an angle of 18.2° with the normal. What is the index of refraction of the transparent material?

Answer 1

n=2.053

Step-by-step explanation:

We will use Snell's Law defined as:

`n_(1)*Sin\theta_(1)=n_(2)*Sin\theta_(2)`

Where n values are indexes of refraction and
`\theta` values are the angles in each medium. For vacuum, the index of refraction in n=1. With this we have enough information to state:

`1*Sin(39.9)=n_(2)*Sin(18.2)`

Solving for
`n_(2)` yields:

`n_(2)=(Sin(39.9))/(Sin(18.2))=2.053`

Remember to use degrees for trigonometric functions instead of radians!