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2014-09-02T21:01:06+05:30

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See diagram.

Light ray is traveling from air to glass and emerging in to air again on the right. The angle of incidence is i and angle of refraction at P is r1. The angle of incidence at P' is r2. the angle of emergence is e.
Delta = D is the angle of deviation from the original path of the ray to the new path after emergence.

D = exterior angle at Q' = i - r1 + e - r2 = i + e - (r1+r2)

A = 360 - (90-Q-90) = 180 - Q in the quadrilateral APQP'.

Q = 180 - r1 - r2 in the triangle AP'P
So, A = r2 + r1

When the angle i is varied, r varies and e varies and D varies. Bu t at one point D is minimum = Dm and at that point i = e and r1 = r2 and the ray PP' is parallel to the base of prism BC.

When D = Dm,
   A = 2 r      Dm = 2 i - A       So, i = (Dm + A) /2

Mu = sin (Dm+A)/2  /  sin A/2


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