An equilateral prism is made up of material of refractive index √3. The angle of minimum deviation of light passing through the prism is_________.
Answers
Answered by
52
Answer:
The answer is 60°
Explanation:
Refractive index of a prism is given by the eq uation.
Refractive index = [Sin{A+DM}/2]/SinA/2
= Sin[{60+Dm}/2]/Sin(60/2)=√3
= Sin{30+(Dm/2)}/Sin30=√3
= Sin{30+(Dm/2)}×2=√3
= 30+(Dm/2)= Sin-1(√3/2)=60°= Dm/2 = 60°–30
Dm =30×2=60°
Answered by
7
Given:
An equilateral prism.
⇒ A = 60°
The refractive index of the prism, μ = √3
To Find:
The angle of minimum deviation of light passing through the prism.
Calculation:
- We know that the refractive index can be given as:
μ = sin {(A+δ)/2} / sin (A/2)
⇒ √3 = sin {(60+δ)/2} / sin (60/2)°
⇒ sin {30° + (δ/2)} = √3 × sin 30°
⇒ sin {30° + (δ/2)} = √3/2
⇒ 30° + (δ/2) = sin⁻¹(√3/2)
⇒ δ/2 = 60° - 30°
⇒ δ = 30° × 2
⇒ δ = 60°
- So, the angle of minimum deviation of light passing throughh the prism is 60°.
Similar questions
Art,
5 months ago
Science,
5 months ago
Math,
5 months ago
Political Science,
10 months ago
Math,
1 year ago