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

Question

Dispersion in a window pane. In Figure (a) below, a beam of white light is incident at angle theta_1 = 75 degree 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 1.555 at the blue end of the spectrum to 1.509 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 pare and (b) when it emerges from the opposite side? (a) Number Units (b) Number Units

Explanation / Answer

from snell's law refraction

n1*sintheta1 = n2*sintheta2

for blue

1*sin75 = 1.555*sintheta2

theta2 = 38.4

for red

1*sin75 = 1.509*sintheta3

theta3 = 39.8

angular spread = theta3 - theta2 = 39.8 - 38.4 = 1.4 degree

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(b)

for blue

n2*sintheta2 = n1*sintheta4

1.555*sin39.8 = 1*sintheta4

theta4 = 75

for red

n2*sintheta3 = n18sintheta5

1.509*sin38.9 = 1*sintheta5

theta5 = 84.5

seperation = 84.5 - 75 = 9.5 degrees

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