Question

What is the index of refraction of the unknown clear substance when a beam of light enters it at an angle of 45.0º, and the observed angle of refraction is 40.3º?

a) 1.12
b) 1.33
c) 1.50
d) 1.78

Answer 1

The index of refraction of the unknown clear substance is approximately 1.50.

Step-by-step explanation:

The index of refraction can be calculated using Snell's law, which 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 velocities of light in the two media:

n1sin(θ1) = n2sin(θ2)

Since the light is entering the unknown substance from water, which has an index of refraction of 1.33, we can rearrange the equation:

n2 = (n1sin(θ1))/sin(θ2) = (1.33sin(45.0°))/sin(40.3°) ≈ 1.50

Therefore, the index of refraction of the unknown substance is approximately 1.50, which corresponds to option c) in the choices given.