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

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 37.7° 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 37.7° with respect to the normal. What is the angle of the refracted ray?

Explanation / Answer

ou can use Snell's law to derive a relationship between refractive index and critical angle c. When light is incident at the critical angle on the interface between the material and air, the angle of refraction is 90deg so has a sin of 1

we can write sin(r)/sin(i) = refractive index (u) (Snell's law is written this way because the ray is incident on the boundary from the direction of the denser medium)

1/sin(c) = u

if c = 41.2deg, u = 1.518

µ(air) . sin i = µ(material ) . sin r

sin r = sin 37.7 / 1.518

r = 23.750

When ray exits material

µ (material) . sin i = µ(air) . sin r

sin r = 1.518. sin 37.7

r = 68.170

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