Question

# A beam of light, traveling in air, strikes a plate of transparent material at an angle...

A beam of light, traveling in air, strikes a plate of transparent material at an angle of incidence of 56.0e. It is observed that the reflected and refracted beams form an angle of 90.0e. What is the index of refraction of this material?

Using snell's law:

n1*sin A1 = n2*sin A2

n1 = refractive index of Air = 1

n2 = refractive index of material = ?

A1 = Angle of incidence with normal = 56 deg

A2 = angle of refraction with normal = ?

We know that

Angle of incidence = Angle of reflection

Angle of Reflection = 56 deg with normal

Angle of reflection with material surface = 90 - 56 = 34 deg

Angle of reflection + Angle of refraction = 90 deg (both with material surface)

Angle of refraction with surface = 90 - 34 = 56 deg

Angle of refraction with normal = 90 - 56 = 34 deg (A2)

So

n2 = n1*sin A1/sin A2

n2 = 1*sin 56 deg/sin 34 deg

n2 = 1.48 = refractive index of material

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