Question

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 690 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 1

Answer:

0.52°

Explanation:

refractive index for blue light, nb = 1.640

Refractive index for red light, nr = 1.595

Angle of incidence, i = 30°

Let the angle of refraction for blue light is rb and the angle of refraction for red light is rR.

By use of Snell's law for blue light

$n_{b}=\frac{Sin i}{Sin r_{b}}$

$1.64=\frac{Sin 30}{Sin r_{b}}$

$1.64=\frac{0.5}{Sin r_{b}}$

$r_{b}=17.75^{\circ}$

By use of Snell's law for red light

$n_{R}=\frac{Sin i}{Sin r_{R}}$

$1.595=\frac{Sin 30}{Sin r_{R}$

$1.595=\frac{0.5}{Sin r_{R}}$

$r_{R}=18.27^{\circ}$

The angle between the two beams, $\theta =r_{R}-r_{b}$

θ = 18.27° - 17.75°

θ = 0.52°