Dear Raza
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 )
we can do an experimental setup to measure A, Dm and create the conditions for minimum deviation of incident light. We can calculate the refractive index for the material that the prism is made of.
Refractive index is not property of Prism. it is of the material.
