If the refractive index of water with respect to air (ₐμw) is 5/3. Calculate the refractive index of air with respect to water (wμₐ).
Topic: Refraction / total internal reflection
Answer
Given: refractive index of water with respect to air, ₐμ_w = 5/3
The two relative refractive indices are reciprocals of each other: ₜμ_a = 1 ÷ (ₐμ_w)
ₜμ_a = 1 ÷ (5/3) = 3/5 = 0.6
Refractive index of air with respect to water = 3/5 (0.6)
Swapping the two media turns the refractive index upside down. That follows from the principle of reversibility of light — a ray traced backwards along its own path behaves the same way.
Read the subscripts carefully, because the whole question is in them. "Refractive index of water WITH RESPECT TO air" means going from air into water; reverse the order and you take the reciprocal.
The answer is less than 1, and that is correct here: going from a denser medium to a rarer one always gives a relative refractive index below 1. A value below 1 is only impossible when it is measured with respect to vacuum or air.