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 ______.

Options

• 180 - 2A

• 90 - A

• 180 + 2A

• 180 - 3A

Answer 1

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.

Explanation:

We known that

`mu = (sin("A"+δm)/2)/(sin("A"/2))`

⇒ `cot  "A"/2 = sin(("A"+δ"m")/1)/(sin("A"/2))`

⇒ `cos("A"/2)=sin(("A"+δ"m")/2)`

⇒ `sin(pi/2-"A"/2)=sin("A"/2+(δ"m")/2)`

⇒ `pi/2-"A"/2="A"/2+(δ"m")/2`

⇒ `pi/2-"A"=(δ"m")/2`

∴ δm = π - 2A