Four students P, Q, R and S traced the path of a ray of light passing through a glass slab for an angle of incidence 40° and measured the angle of refraction. The values as measured them were 18°; 22°; 25° and 30° respectively. The student who has performed the experiment methodically is

According to Snell's law of refraction, the ratio of the sine of the angle of incidence ($i$) to the sine of the angle of refraction ($r$) is constant for a given pair of media, which is the refractive index ($n$) of the second medium with respect to the first:

$$\frac{\sin i}{\sin r} = n$$

For light travelling from air to glass, the refractive index of glass is approximately $n \approx 1.5$.

Given the angle of incidence $i = 40^\circ$:

$$\sin(40^\circ) \approx 0.6428$$

Using Snell's law:

$$\sin r = \frac{\sin(40^\circ)}{1.5} \approx \frac{0.6428}{1.5} \approx 0.4285$$

Taking the inverse sine:

$$r = \arcsin(0.4285) \approx 25.37^\circ \approx 25^\circ$$

Thus, the student who measured $25^\circ$ (Student R) performed the experiment methodically and obtained the most accurate result.

• Distractor A (Student P, $18^\circ$): This value is too low and would correspond to an unrealistically high refractive index of about $2.08$.
• Distractor B (Student Q, $22^\circ$): This value corresponds to a refractive index of about $1.72$, which is higher than standard crown glass.
• Distractor D (Student S, $30^\circ$): This value corresponds to a refractive index of $1.29$, which is closer to water ($1.33$) than glass.