Question

Derivation of formula for refractive index of a prism

Answer 1

Answer:

The angle of deviation D = angle bent by emerging ray with respect to incident ray. D is the exterior angle of the triangle PP'Q'. It is sum of two interior angles.

See derivation in the diagram.

A + Q +90 + 90 = 360 and Q+r1+r2 = 180

So A = r1 + r2

D = (i-r1) + ( e-r2) = (i  + e) - (r1 +r2)

D = i + e - A

Vary i and then e varies. At one point D is minimum and at that point i = e.

When D is minimum and = Dm, we see that i = e and r1 = r2 = r

D = 2 i - A

i = (D+A)/2

r = A/2          as r1+r2 = 2 r  = A.

μ = sin i / sin r  = [ sin (A+Dm)/2 ]  / (  sin A/2 )

Explanation: