Answer:
37°
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, [tex]\theta_c[/tex]) 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:
[tex]\theta_c = sin^{-1} (\frac{n_2}{n_1})[/tex]
where
[tex]n_1[/tex] is the index of refraction of the 1st medium
[tex]n_2[/tex] is the index of refraction of the 2nd medium
In order to have total internal reflection, it must be [tex]n_1>n_2[/tex].
In this problem:
[tex]n_1=2.42[/tex] is the index of refraction of diamond
[tex]n_2=1.46[/tex] is the index of refraction of quartz
Substituting, we find the value of the critical angle:
[tex]\theta_c=sin^{-1}(\frac{1.46}{2.42})=37^{\circ}[/tex]
