Question

The indices of refraction for violet light (λ = 400 nm) and red light (λ = 700 nm) in diamond are 2.46 and 2.41, respectively. A ray of light traveling through air strikes the diamond surface at an angle of 51.5 ∘ to the normal.

A) Calculate the angular separation between these two colors of light in the refracted ray.

Answer 1

Answer 2

From Snell's law:

\(n_{i} \sin i=n_{r} \sin r\)

\(\sin r=\frac{n_{i}}{n_{r}} \sin i\)

The angle of refraction of violet light,

\(\sin r_{v}=\frac{1}{2.46} \sin 51\)

\(\begin{aligned} &=0.315 \\ r_{v} &=18.4^{\circ} \end{aligned}\)

The angle of refraction for red light

\(\sin r_{r}=\frac{1}{2.41} \sin 51\)

\(\begin{aligned} &=0.322 \\ r_{v} &=18.8^{\circ} \end{aligned}\)

The angular separation is given by:

\(\Delta \theta=r_{v}-r_{r}\)

\(=0.4^{\circ}\)