The refracting angle of a prism is A and refractive index of the material of the prism is cot ( A / 2). Then the angle of minimum deviation will be -

Question

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

Tardigrade Admin · Accepted Answer

μ=( sin (( A +δ m /2))/ sin ( A )2) μ= cot ( A /2) ⇒ sin (( A +δ m /2))= cos ( A /2) δ m =180-2 A

Q. The refracting angle of a prism is $A$ and refractive index of the material of the prism is $cot (A /2)$ . Then the angle of minimum deviation will be -

$180 - 2 A$

$90 - A$

$180 + 2 A$

$180 - 3 A$

$μ = \frac{s i n ( \frac{A + δ _{m}}{2} )}{s i n \frac{A}{2}}$
$μ = cot \frac{A}{2}$
$\Rightarrow sin (\frac{A + δ _{m}}{2}) = cos \frac{A}{2}$
$δ_{m} = 180 - 2 A$

Q. The refracting angle of a prism is A and refractive index of the material of the prism is cot(A/2). Then the angle of minimum deviation will be -

180−2A

90−A

180+2A

180−3A