A narrow beam of light containing orange (610 nm) and blue (470 nm) wavelengths goes from polystyrene to air, striking the surface at a 28.5° incident angle. What is the angle (in degrees) between the colors when they emerge?

Answer: The angle between the two colours when they emerge is 0.4°

Explanation:

The refracting angle for different colors knowing its refractive index can be calculated using Snell's law.

Ni * sin α = Nr * sinβ

Where Ni is the refractive index for light in incident medium

α is the angle the incident makes with normal

Nr is the refractive index for light in the refractive medium

β is the angle the refracted makes with the normal

Making β the subject

β = arcSin (Ni * sinα) / Nr

For Orange color

The value of refractive index in polystyrene medium is 1.490, that is Ni = 1.490

α is 30° and Nr is the refractive index of air = 1

β = arcSin (1.490*sin30°) / 1

β = 48.15°

For Blue color

The value of refractive index in polystyrene medium is 1.499, that is Ni = 1.499

α is 30° and Nr is the refractive index of air = 1

β = arcSin (1.499*sin30°) / 1

β = 48.55°

The angle between the two colours is the difference in the angles of their refracted rays

48.55-48.15=0.4°