Question

Calculate the critical angle between diamond (n = 2.42) and quartz (n = 1.46)?

23°
37°
52°
60°

Answer 1

37 degrees

Step-by-step explanation:

Took the test in FLVS and got it right.

Answer 2

37°

Step-by-step explanation:

Total internal reflection is a phenomenon that occurs when a ray of light is moving from a medium with higher index of refraction to a medium with lower index of refraction; in this case, there exist a value of the angle of incidence (called critical angle,
`\theta_c`) above which no refraction occurs, and all the light is reflected back into the original medium.

The value of the critical angle between two mediums is given by the formula:

`\theta_c = sin^(-1) ((n_2)/(n_1))`

where

`n_1` is the index of refraction of the 1st medium

`n_2` is the index of refraction of the 2nd medium

In order to have total internal reflection, it must be
`n_1>n_2`.

In this problem:

`n_1=2.42` is the index of refraction of diamond

`n_2=1.46` is the index of refraction of quartz

Substituting, we find the value of the critical angle:

`\theta_c=sin^(-1)((1.46)/(2.42))=37^(\circ)`