Question

the angel of deviation of the prism is (180-2A). It's critical angle Will be​

Answer 1

Answer: its answer will be cot A/2

Explanation:

Please mark brilliant

Answer 2

Given:

The angel of deviation of the prism, δ = (180-2A)

To Find:

The critical angle of the prism.

Calculation:

- The refractive index of the prism is given as:

μ = sin {(A + δ)/2} / sin (A/2)

⇒ μ = sin {(A + 180 - 2A)/2} / sin (A/2)

⇒ μ = sin {(180 - A)/2} / sin (A/2)

⇒ μ = sin {90 - (A/2)} / sin (A/2)

⇒ μ = cos (A/2) / sin (A/2)

⇒ μ = cot (A/2)

- The critical angle is given as:

sin $i_{c}$ = 1 / μ

⇒ sin $i_{c}$ = 1 / cot (A/2)

⇒ sin $i_{c}$ = tan (A/2)

⇒ $i_{c}$ = sin⁻¹ {tan (A/2)}

- So, the critical angle of the prism is sin⁻¹ {tan (A/2)}.