Question

A thin prism produces an angular dispersion of 18'. If the refracting angle of prism is 2° and the R.I. of its material for violet light is 1.74, calculate the R.I. of its material for red light.

Answer 1

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.