Answer:
76.78°
Step-by-step explanation:
According to Snell's law
[tex]\bf \displaystyle\frac{sin(\theta_2)}{sin(\theta_2)}=\displaystyle\frac{n_1}{n_2}[/tex]
The critical angle of incidence [tex]\bf \theta_1[/tex] occurs when [tex]\bf \theta_2=90^{o}[/tex]
The index of refraction of air can be considered 1. The index of refraction of diamond is 2.417
Solving for [tex]\bf \theta_1[/tex]
[tex]\bf \displaystyle\frac{sin(90^{o})}{sin(\theta_1)}=\displaystyle\frac{2.417}{1}\Rightarrow sin(\theta_1)=\displaystyle\frac{1}{2.417}\Rightarrow sin(\theta_1)=0.41374\Rightarrow\\\\\Rightarrow \theta_1=arcsin(0.41374)\Rightarrow \theta_1=0.42656\;rad\Rightarrow \boxed{\theta_1=76.78^{o}}[/tex]