Question

The refracting angle of a prism is A, and refractive
index of the material of the prism is cot (A/2). The
angle of minimum deviation is:
(A) 180° - 2A
(B) 90° - A
(C) 180° + 2A
(D) 180° - 3A

unnessary answers ate reported
only I need correct answer with explanation ✌​

Answer 1

μ=(sin(A+D)/2)÷sinA/2=cotA/2

sin(A+D)/2=cosA/2

(A+D)/2=3.14/2-A/2

D=180-2A

option is (A)

Answer 2

↧↧↧↧↧↧↧↧↧↧↧↧↧↧↧↧

The formula for refractive index of the materaial of a prism is:

n=[sin(A+dm)/2]/sin(A/2)………………….(1)

dm=angle of minimum deviation.

Now, n=cot(A/2)=cos(A/2)/sin(A/2). Using this fact in eq.(1),

cos(A/2)=sin[(A+dm)/2],

Cos (A/2) = Sin( 90° - A/2)

sin(90° - A/2)=sin(A/2+dm/2)

Therefore,

90° - A/2= ( A + dm)/2= A/2 + dm/2,

==> 90° - A= dm/2,

==> dm = 180° - 2 A.

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