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

ID: 1461358 • 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= 41.0° what is the index of refraction of the material?

A light ray strikes this material (from air) at an angle of 36.8° 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 36.8° with respect to the normal. What is the angle of the refracted ray?

Explanation / Answer


apply snells law as na sin A = nb sin B

where na and nb are the refractive index

A is the angle of incidence and B is the angle of refraction

so

here for critical angle B = 90 deg

A = 41

na = 1

nb = ?

so

nb/na = 1/sin 41

nb = 1.524

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as angle of incidence = angle of reflection


here angle of reflection = 36.8 deg

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sinB = 1 * sin 36.8/1.524

sin B = 0.393

B - refracted angle = 23.14 deg

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na * sin 36.8 = nb * sin B

sin B = 1.52 sin 36.8

sin B = 0.910

B = 65.5 deg

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