Q18E - University Physics with Modern Physics

Question

A beam of light is traveling inside a solid glass cube that has index of refraction 1.62. It strikes the surface of the cube from the inside. (a) If the cube is in air, at what minimum angle with the normal inside the glass will this light not enter the air at this surface? (b) What would be the minimum angle in part (a) if the cube were immersed in water?

Step-by-Step Solution

Answer

1. The minimum angle with the normal side when the cube is in the air $38.118°$
2. The minimum angle when the cube is immersed in water $55.37°$

Step 1: Snell’s law

Snell's law determines the degree of refraction as well as the relationship between the angle of incidence, angle of refraction, and refractive indices of two media.

Here;

Critical Angle-Beyond which light rays traveling through a thicker media to the surface of a less dense medium is no longer refracted but completely reflected

Total Internal Reflection-When the angle of incidence surpasses the critical angle, a light ray reaches an interface with a less dense material and is completely reflected.

Step 2: Minimum angle with the normal side when cube in air

Applying Snell’s law;

Hence, the minimum angle with the normal side when the cube is in the air $38.118°$

Step 3: Minimum angle when cube immersed in water

Applying Snell’s law;

Hence, the minimum angle when the cube is immersed in water $55.37°$