A light ray passes from water (refractive index ( n1 = 1.33 )) into diamond (refractive index ( n2 = 2.42 )). If the angle of incidence in water is ( 300 ), what is the angle of refraction in diamond?单项选择题
A
a. 19.20
B
b. 22.80
C
c. 15.50
D
d. 25.40

Question

A light ray passes from water (refractive index ( n1 = 1.33 )) into diamond (refractive index ( n2 = 2.42 )). If the angle of incidence in water is ( 300 ), what is the angle of refraction in diamond?

BlackTom AI · Accepted Answer

We start from Snell's law for refraction: n1 sin(theta1) = n2 sin(theta2).
Given: n1 = 1.33, theta1 = 30 degrees, n2 = 2.42.
Compute sin(theta2): sin(theta2) = (n1 * sin(theta1)) / n2.
sin(30°) = 0.5, so sin(theta2) = (1.33 * 0.5) / 2.42 = 0.665 / 2.42 ≈ 0.2748.
Now find theta2: theta2 ≈ arcsin(0.2748) ≈ 15.9 degrees. This is the expected angle of refraction in diamond.
Let's evaluate each option with this calculation in mind.

Option a: 19.20 degrees. If you take theta2 = 19.20°, sin(19.20°) ≈ 0.329, which would imply a different relation than the given n1, n2 values. Therefore this is not consistent with Snell's law for the provided indices and incident angle.

Option b: 22.80 degrees. sin(22.80°) ≈ 0.388, again not matching the 0.2748 value obtained from Snell's law with the given data. This option is incorrect for the same reason: it doesn't satisfy n1 sin(theta1) = n2 sin(theta2).

Option c: 15.50 degrees. sin(15.50°) ≈ 0.267. This is very close to the 0.2748 value we computed; small differences can arise from rounding during intermediate steps. This option is plausible given typical rounding practices in problems of this type.

Option d: 25.40 degrees. sin(25.40°) ≈ 0.430, which is significantly different from 0.2748, so this choice does not satisfy the equation for the given indices and incident angle.

In summary, the correct refraction angle predicted by Snell’s law is about 15.9°, which aligns best with option c when considering typical rounding in problems. The other options yield sine values that are inconsistent with the computed sin(theta2) from the given n1, n2, and theta1, explaining why they do not fit the scenario.

A light ray passes from water (refractive index ( n1 = 1.33 )) into diamond (refractive index ( n2 = 2.42 )). If the angle of incidence in water is ( 300 ), what is the angle of refraction in diamond?单项选择题

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