Dispersion in a window pane. In Figure (a) below , a beam of white light is inci

Question

Dispersion in a window pane. In Figure (a) below , a beam of white light is incident at angle ?1 = 81o on a common window pane (shown in cross section). For the pane's type of glass, the index of refraction for visible light ranges from 1.538 at the blue end of the spectrum to 1.511 at the red end. The two sides of the pane are parallel. What is the angular spread of the colors in the beam (a) when the light enters the pane and (b) when it emerges from the opposite side? (Hint: When you look at an object through a window pane, are the colors in the light from the object dispersed as shown in, say, Figure (b)?)

Explanation / Answer

Here,

theta1 = 81 degree

n1 = 1.511

n2 = 1.538

n = 1

for the red light

n * sin(theta1) = n1 * sin(r1)

1 * sin(81) = 1.511 * sin(r1)

r1 = 40.81 degree

for the blue light

n * sin(theta1) = n2 * sin(r2)

1 * sin(81) = 1.538 * sin(r2)

r2 = 39.96 degree

angular spread = r2 - r1

angular spread = 40.81 - 39.96

angular spread = 0.855 degree

the angular spread is 0.855 degree

b)

when the lights exits into the air

angular spread = 2 * initial angular spread

angular spread = 2 * 0.855

angular spread = 1.71 degree

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