The refractive index of waters is 1.33 Calculate the critical angle State whether total internal refraction occurs at 50°

The formula for the critical angle ($\theta_c$) is given by:

$$\sin(\theta_c) = \frac{1}{n}$$

where $n$ is the refractive index.
Given $n = 1.33$.

Substitute the value of $n$:

$$\sin(\theta_c) = \frac{1}{1.33}$$ $$\sin(\theta_c) \approx 0.75188$$

To find $\theta_c$, take the inverse sine:

$$\theta_c = \arcsin(0.75188)$$ $$\theta_c \approx \boxed{\text{48.75°}}$$

Total internal reflection occurs when the angle of incidence is greater than the critical angle.
The calculated critical angle ($\theta_c$) is approximately $48.75^\circ$.
The given angle of incidence is $50^\circ$.

Since $50^\circ > 48.75^\circ$, total internal reflection does occur.

$$\text{Total internal reflection occurs at 50° because } 50^\circ > 48.75^\circ$$