A plate of glass with parallel faces having a refractive index of 1.57 is restin

Question

A plate of glass with parallel faces having a refractive index of 1.57 is resting on the surface of water in a tank. A ray of light coming from above in air makes an angle of incidence 33.5? with the normal to the top surface of the glass. (Figure 1)

What angle ?3 does the ray refracted into the water make with the normal to the surface? Use 1.33 for the index of refraction of water.

Express your answer in degrees.

A plate of glass with parallel faces having a refractive index of 1.57 is resting on the surface of water in a tank. A ray of light coming from above in air makes an angle of incidence 33.5? with the normal to the top surface of the glass. (Figure 1) What angle ?3 does the ray refracted into the water make with the normal to the surface? Use 1.33 for the index of refraction of water. Express your answer in degrees.

Explanation / Answer

Let the incident ray at the air glass boundary make an angle ?1 with the normal

Let the refracted ray at the air glass boundary make an angle ?2 with the normal

Therefore, the incident ray at the glass water interface makes an angle ?2 with the normal

and let the refracted ray at the glass water interface make an angle ?3 with the normal to the surface

Use Snell's law at the air glass interface:

n1sin?1 = n2sin?2 ...(i)

n1, n2 are for air and glass

At the glass-water interface we have

n2sin?2 = n3sin?3...(ii)

n3 is the index of refraction for water

From equations (i) and (ii), we get

n1sin?1 = n3sin?3

n1 = 1 or air
n3 = 1.33 for water
?1 = 33.5

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