(a) A narrow beam of light containing yellow (580 nm) and green (550 nm) wavelengths goes from polystyrene to air, striking the surface at a 30.0°30.0° incident angle. What is the angle between the colors when they emerge?

0.043°

Explanation:

Snell's law States that the ratio of the angle of incidence to angle of refraction is a constant for a given pair of media.

n = sin(i)/sin(r)

n1/n2 = sin(i)/sin(r)

For the green polystyrene

n2 = refractive index of green polystyrene = 1.493

n1 = refractive index of air = 1

1/1.493= sin30°/sin(r1)

sin(r1) = sin30°×1.493

sin(r1) = 0.5×1.493

sin(r1) = 0.7465

r1 = sin^-1(0.7465)

r1 = 48.288°

For the yellow polystyrene

n2 = refractive index of yellow polystyrene = 1.492

n1 = refractive index of air = 1

1.492/1= sin30°/sin(r2)

sin(r2) = sin30°×1.492

sin(r2) = 0.5×1.492

sin(r2) = 0.746

r2 = sin^-1(0.746)

r2 = 48.245°

The angle between the colors when they emerge = r1-r2

angle between the colors when they emerge = 48.288°-48.245°

angle between the colors when they emerge = 0.043°