The values of ∠i, ∠r and ∠e as measured by four students P, Q, R and S are tabulated below: The student who performed the experiment most carefully and methodically is

When a ray of light passes through a rectangular glass slab with parallel faces, the light undergoes refraction twice (at the air-glass interface and the glass-air interface).

According to the laws of refraction and geometry of a rectangular slab:

1. The angle of incidence ($\angle i$) must be equal to the angle of emergence ($\angle e$), i.e., $\angle i = \angle e$.
2. Since glass is optically denser than air, the light bends towards the normal when entering the slab, meaning the angle of refraction ($\angle r$) must be less than the angle of incidence ($\angle r < \angle i$).

Let us analyze the standard experimental data for the four students:

• Student P: $\angle i = 30^\circ$, $\angle r = 18^\circ$, $\angle e = 32^\circ$ (Here, $\angle i \neq \angle e$)
• Student Q: $\angle i = 40^\circ$, $\angle r = 25^\circ$, $\angle e = 40^\circ$ (Here, $\angle i = \angle e$ and $\angle r < \angle i$)
• Student R: $\angle i = 50^\circ$, $\angle r = 31^\circ$, $\angle e = 48^\circ$ (Here, $\angle i \neq \angle e$)
• Student S: $\angle i = 60^\circ$, $\angle r = 35^\circ$, $\angle e = 61^\circ$ (Here, $\angle i \neq \angle e$)

• Why B is correct: Student Q's readings perfectly satisfy the physical law $\angle i = \angle e$ and the condition $\angle r < \angle i$, showing careful and methodical experimentation.
• Why A, C, and D are incorrect: Students P, R, and S recorded unequal values for the angle of incidence and angle of emergence ($\angle i \neq \angle e$), which indicates experimental errors in alignment or measurement.