Find the dispersion for red and violet light when both are incident on the flat surface of the liquid at an angle of 43.00 degrees to the normal.

Question

The index of refraction for red light in a certain liquid is 1.320; the index of refraction for violet light in the same liquid is 1.333. Find the dispersion θ_v-θ_r  for red and violet light when both are incident on the flat surface of the liquid at an angle of 43.00 degrees to the normal.

Answer 1

To find the dispersion, you need to find the angle of refraction for each light color using Snell's Law:

n₁ sin θ₁ = n₂ sin θ₂

where n is the index of refraction for each medium (air, liquid) and θ is the angle from the normal the light ray makes within the medium.

The two beams enter the liquid from air at the same angle, 43° to the normal. So for red light:

1 sin 43°= 1.32 sin θ₂

θ₂ =sin^-1 (sin 43°/1.32) = 31.1°

We repeat the same process for the violet light:

1 sin 43°= 1.333 sin θ₂

θ₂ =sin^-1 (sin 43°/1.333) = 30.8°

The dispersion, then is 31.1° - 30.8° = 0.3°