Question

At what minimum angle will you get total internal reflection of light traveling in water and reflected from ice?

Short answer

When light travels through water and is reflected by ice, the critical angle is $79.{11}^{°}$.

Step-by-step solution

Definition of angle of refraction

At the point of refraction, the angle formed by a refracted beam and a line drawn normal to the interface between two media.

Finding the minimum angle

Let us solve the given problem,

The expression to find the critical angle is,

${\theta }_{\circ }={\sin }^{-1}\left(\frac{n_2}{n_1}\right)$

Here,

• ${\theta }_{\circ }$is a critical angle.
• $n_1$is the index of refraction of medium 1.
• $n_2$is the index of refraction of medium 2.

The refractive index of water is 1.333 and of ice is 1.309.

Substituting 1.333 for n₁ and 1.309 for n₂ to calculate the critical angle,

$$\begin{gathered} {\theta }_{\circ }={\sin }^{-1}\left(\frac{1.309}{1.333}\right) \\ =79.{11}^{°} \end{gathered}$$

Therefore, the crucial angle when light flows through water and is reflected by ice is$79.{11}^{°}$.