A student very cautiously traces the path of a ray through a glass slab for different values of the angle of incidence ($\angle i$). He then measures the corresponding values of the angle of refraction ($\angle r$) and the angle of emergence ($\angle e$) for every value of the angle of incidence. On analysing these measurements of angles, his conclusion would be

When a ray of light passes through a rectangular glass slab:

1. At the first interface (Air to Glass): Light travels from an optically rarer medium (air) to an optically denser medium (glass). Consequently, the refracted ray bends towards the normal. Therefore, the angle of refraction ($\angle r$) is less than the angle of incidence ($\angle i$):

$$\angle i > \angle r$$

1. At the second interface (Glass to Air): Light travels from an optically denser medium (glass) to an optically rarer medium (air). The emergent ray bends away from the normal. For a rectangular glass slab with parallel opposite faces, the extent of bending of the ray of light at the opposite parallel faces is equal and opposite. Thus, the emergent ray is parallel to the incident ray, meaning the angle of emergence ($\angle e$) is equal to the angle of incidence ($\angle i$):

$$\angle i = \angle e$$

Combining these two relations gives:

$$\angle i = \angle e > \angle r$$

• Option A is incorrect because $\angle e$ is equal to $\angle i$, not smaller than $\angle r$.
• Option B is correct as it accurately represents the relationship $\angle i = \angle e > \angle r$.
• Option C is incorrect because $\angle r$ must be smaller than $\angle i$ when light enters a denser medium.
• Option D is incorrect because $\angle r$ is smaller than $\angle i$, not larger.