A certain kind of glass has an index of refraction of 1.640 for blue light of wavelength 440 nm and an index of 1.595 for red light of wavelength 670 nm. If a beam containing these two colors is incident at an angle of 30.0° on a piece of this glass, what is the angle between the two beams inside the glass?

Answer: 18.27°

Explanation:

Given

Index of refraction of blue light, n (b) = 1.64

Wavelength of blue light, λ (b) = 440 nm

Index of refraction of red light, n (r) = 1.595

Wavelength of red light, λ (r) = 670 nm

Angle of incident, θ = 30°

Angle of refraction of red light is

θ (r) = sin^-1 [ (n (a) * sin θ) / n (r) ], where n (a) = index of refraction of air = 1

So that,

θ (r) = sin^-1 [ (1 * sin 30) / 1.595]

θ (r) = sin^-1 (0.5 / 1.595)

θ (r) = sin^-1 0.3135

θ (r) = 18.27°