Question

What is the critical angle if a ray of light in Quartz (n=1.46) is headed into Water (n=1.33)?48.8°65.6°43.2⁰0.911⁰

Answer 1

Critical angle is a special case of angle of incidence for which angle of refraction is 90 degree.

Now using Snell's law

$n_1\sin\theta_1=n_2\sin\theta_2$

Here

$\begin{gathered} n_1=\text{ refractive index of incident medium;} \\ n_2=\text{refract}\imaginaryI\text{ve index of refracting medium;} \\ \theta_1=\text{ angle of incidence;} \\ \theta_2=\text{ angle of refraction;} \end{gathered}$

Now according to problem

$\begin{gathered} 1.46\sin\theta_1=1.33\sin90\degree; \\ \sin\theta_1=\text{ }\frac{1.33}{1.46}\begin{cases}sin90={1} \\ \end{cases} \\ \theta_1=\sin^{-1}(0.91095)=\text{ 65.6}\degree \end{gathered}$

Final answer is 65.6°