Light traveling through air strikes the surface of a material at an incident ang

Question

Light traveling through air strikes the surface of a material at an incident angle of 70 degree. a. Sketch the light that is reflected from the top surface, and refracted into the n = 1.8 material. Then sketch the light that reflects off the surface between the 1.8 material and the 1.2 material, and the light that is refracted into the n = 1.2 material. Then sketch the light that reflects off the surface between the n = 1.2 material and the air, and then the light that refracts into the air. (It's ok if the angles aren't what you calculate below, they just have to show relative closeness to the normal.) b. What is the angle the refracted light makes with the normal in the n = 1.8 material? c. What is the angle refracted light makes with the normal in the n = 1.2 material? d. What is the angle the refracted light makes with normal in the air below the two layers?

Explanation / Answer

a] The reflected light from air to n = 1.8 medium will bear an angle of 70 degrees with normal. The refracted light will get transmitted inside the medium and have an angle of refraction less than 70 degrees (bending towards the normal).

This light will continue to travel downwards and hits an interface of n = 1.2 surface and n = 1.8 surface. The refracted light will bend away from the normal.

b] n1sin70 = n2sin(theta)

[Snell's law]

=> theta = sin-1(sin70/1.8) = 31.47o

this is the angle of refraction which the light makes with the normal in n = 1.8 material.

c] 1.8sin31.47 = 1.2sin(theta)

=> theta = sin-1(1.8sin31.47/1.2) = 51.54o

this is the angle of refraction which the light makes with the normal in n = 1.2 material.

d] 1.2sin51.54 = 1sin(theta)

=> theta = sin-1(1.2sin51.54) = 70o

this is the angle of refraction which the light makes with the normal in the air below both the layers.

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