Question

A diamond bottle is submerged in an alcohol solution. A ray of light travels through the alcohol at an angle of 36 degrees. The light ray has a wavelength of 650 nm.

a) Find the angle of refraction when the light hits the diamond bottle, as it comes from the alcohol. (show work/equation used)

Calculate the speed as the light propagates in the alcohol? (show work/equation used)

Is the light speeding up or slowing down?

b) FInd the angle of reflection, as the light hits the alcohol (show work)

c) Now find the critical angle as the light penetrates the diamond and propagates to the air inside of it (show work)

Answer 1

N_diamond = 2.42

N_alcohol = 1.36

incident angle = 36 degree

wavelength = 650 nm

A) using snell's law

N_diamond* Sin(r) = N_alcohol * Sin(i)

2.42 * Sin(r) = 1.36 * Sin(36)

Sin(r) = 0.3303

r = 19.28 degree

{Angle of refraction}

Speed of light in alcohol = c /N_alcohol

= 3 * 10^ 8 /1.36

= 2.205 * 10^8 m/s

The speed of light is slowing down

b)

angle of reflection is always equal to angle of incidence

Therefore, angle of reflection = 36 degrees

c) Critical angle (C)

using formula,

Sin(C) = N_air/N_diamond

Sin(C) = 1/2.42

C = 24.4 degrees
Therefore critical angle = 24.4 degree

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