Question

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 by them were 18°; 22°; 25° and 30° respectively. The student who has performed the experiment methodically is (A) P (B) Q (C) R (D) S

Answer 1

The student R has performed the experiment methodically. The reason can be explained using Snell's law. According to Snell's law, sini*sinr=μg Here, i = Angle of incidence r = Angle of refraction μg = Refractive index for glass The angle of refraction measured by student R is most appropriate as it verifies the Snell's law. Given: i = 40o The angle of refraction measured by student R, r = 25o. Also, sin40o = 0.642 sin25o = 0.422 Now, sin40osin25o=0.6420.422=1.52 The refractive index for glass is 1.5; it verifies the result derived above. Hence, the correct option is C. Disclaimer: The values of sin40o and sin25o can be obtained using trigonometric tables.

Answer 2

The angle of refraction of light passing through a glass slab depends on the angle of incidence and the refractive index of the glass. If the refractive index of the glass slab is constant, the angle of refraction should be the same for all the students, regardless of who performed the experiment methodically.

However, the measured values of the angle of refraction by the four students are different, indicating that there may have been some errors or inconsistencies in their measurements.

To determine which student performed the experiment methodically, we can compare their measured values with the theoretical value of the angle of refraction calculated using Snell's law.

Snell's law states that the ratio of the sine of the angle of incidence to the sine of the angle of refraction is equal to the ratio of the refractive indices of the two media:

sin(i) / sin(r) = n

where i is the angle of incidence, r is the angle of refraction, and n is the refractive index of the glass slab.

Assuming that the angle of incidence is 40° and the refractive index of the glass slab is a constant value, we can calculate the theoretical value of the angle of refraction using Snell's law. For example, if we assume that the refractive index of the glass slab is 1.5 (a common value for glass), we can calculate the theoretical value of the angle of refraction as follows:

sin(40°) / sin(r) = 1.5

sin(r) = sin(40°) / 1.5

r = sin^-1(sin(40°) / 1.5)

r ≈ 24.2°

Comparing the theoretical value of the angle of refraction with the measured values of the four students, we can see that the student who is closest to the theoretical value is student R, who measured the angle of refraction as 25°. Therefore, student R is likely to have performed the experiment methodically.

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