Please Show work The refractive index of a transparent material can be determine

Question

Please Show work

The refractive index of a transparent material can be determined by measuring the critical angle when the solid is in air. If theta_c= 41.3 degree what is the index of refraction of the material? A light ray strikes this material (from air) at an angle of 31.9 degree 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 31.9 degree with respect to the normal. What is the angle of the refracted ray?

Explanation / Answer

part a )

mu = 1/sintheta

mu = 1.515

part b )

angle of incidene = angle of reflection

= 31.9 degree

part c )

n1sintheta1 = n2 sintheta2

sin theta 2 = n1sintheta1/n2

n1 = 1

theta 2 = sin^-1(sintheta1/n2)

theta 2 = 20.41 degree

part d )

n1sintheta1 = n2 sintheta2

n2 = 1 air

theta2 = 53.2 degree

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