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

Answer:

n=2.053

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:

$n_{2}=\frac{Sin(39.9)}{Sin(18.2)}=2.053$

Remember to use degrees for trigonometric functions instead of radians!