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

Answer 1

Answer:

a) 180°-2A

Explanation:

Refractive index of prism = A (Given)

Refractive index of material of prism = cot(A/2) (Given)

Formula to calculate the refractive index of material of a prism is:

n=[sin(A+dm)/2]/sin(A/2) --- (1)

where dm is the angle of minimum deviation.

n = cot (A/2 )= cos(A/2)/sin(A/2).

Using the above equation 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°-2A

Thus, The angle of minimum deviation is 180°-2A.