For a particular pair of transparent medium and a. particular colour of light when ray of light refracts from one medium to another, then if the angle of incidence is i and the angle of refraction is r, then [sin i/sin r] will be a constant and it is called refractive index of the second medium with respect to the first medium for that colour of light. It is expressed by n.
If the my of light enters in the medium b from medium a then the refractive index of sin i medium b with respect to a is, anb = [sin i/sin r]
Mathematical example: When light refracts from air to water, the angle of incidence is 30° and angle of refraction is 19°. Find the refractive index of water with respect to air.
Angle of incidence, i = 30°
Angle of refraction, r = 19°
Refractive index of water with respect to air, anw =?
[sin i/sin r] = n
So, anw = [sin i/sin r] = [sin 30°/sin 19°]
= 0.5 / 0.325 = 1.538
Ans: Refractive index: 1.538