Question

A beam of light passes from zircon to quartz at an incident angle of 8°. What is the angle of refraction?

Answer 1

`9.4^@`, rounded to one decimal place.

Explanation:

Refractive index of Zircon and Quartz varies as below

Zircon: `1.81 - 2.024`
Quartz: `1.544 - 1.553`

For this problem the refractive indices of samples are assumed as lowest.

From Snell's law we know that when a beam passes from a medium `1` having refractive index `n_1` making and angle `theta_1` to medium `2` having refractive index `n_2`, angle of refraction `theta_2` is given by the equation

`n_1 sin theta_1 = n_2 sin theta_2`

Inserting given values we get

`1.81 sin 8^@= 1.544 sin theta_2`
`=> sin theta_2=(1.81 sin 8^@)/1.544`
`=> theta_2=sin^-1 ((1.81 sin 8^@)/1.544)`
`=9.4^@`, rounded to one decimal place.