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The refractive index of a transparent material can be determined by measuring th

ID: 1446059 • Letter: T

Question

The refractive index of a transparent material can be determined by measuring the critical angle when the solid is in air. If c= 41.2° what is the index of refraction of the material?

A light ray strikes this material (from air) at an angle of 35.2° with respect to the normal of the surface. Calculate the angle of the reflected ray (in degrees).
Calculate the angle of the refracted ray (in degrees).
Assume now that the light ray exits the material. It strikes the material-air boundary at an angle of 35.2° with respect to the normal. What is the angle of the refracted ray?

Explanation / Answer

snell's law

n1*sin A1 = n2*sin A2

A.

When light is incident at the critical angle on the interface between the material and air, the angle of refraction is given by 90 deg

sin 90 = 1

critical angle = 41.2 deg

for air n = 1

using snell's law

n1*sin A1 = n2*sin A2

n1 = 1*sin 90 deg/(sin 41.2 deg)

n1 = 1/sin 41.2 deg

n1 = 1.518

B.

Angle of incidence = angle of reflection

Angle of refliection = 35.2 deg

C. Angle of refraction is given by snell's law

in this case n1 = 1 (air)

A1 = 35.2 deg

n2 = 1.518

A2 = ?

from snell's law

A2 = arcsin ((1*sin 35.2 deg)/1.518)

A2 = 22.31 deg

D. this time

n1 = 1.518

A1 = 35.2 deg

n2 = 1

A2 = ?

A2 = arcsin ((1.518*sin 35.2 deg)/1)

A2 = 61.04 deg

let me know if you have any doubt.

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