Question

1. A beam of light moving through the air strikes the surface of a transparent medium at an angle of 54º to the normal. If the beam continues into the medium at an angle of 27º to the normal, what is the approximate refractive index of this medium?

2.After repeated trials, an investigator determines that when violet light travels through a gem and encounters an interface with air, the smallest angle of incidence that will allow for total internal reflection is approximately 35º. The investigator would be justified in calculating which of the following as the refractive index of the gem?

Answer 1

1.

Using snell's law:

n1*sin A1 = n2*sin A2

n1 = refractive index of Air = 1

n2 = refractive index of unknown medium = ?

A1 = Angle of incidence = 54 deg

A2 = angle of refraction = 27 deg

So,

n2 = n1*sin A1/sin A2

n2 = 1*sin 54 deg/sin 27 deg

n2 = 1.782 = refractive index of medium

2.

when violet light is traveling from gem to air

using snell's law:

n1*sin A1 = n2*sin A2

n2 = refractive index of air = 1

A2 = 90, since Total internal reflection

n1 = n2*sin A2/sin A1

A1 = angle of incidence = 35 deg

n1 = 1*sin 90 deg/sin 35 deg = 1.74

n1 = refractive index of gem = 1.74

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