Question

A Ray of light while passing through a prism suffers a minimum deviation of 40, calculate the RI fo the material of prism if the angle is 60. [ given: sine 50= 0.7660, sine 30= 0.5]

Answer 1

Angle of deviation is 37.2° and angle of incidence is 48.6°

For a prism, refractive index μ is given as:

μ = [sin ([A + δ]/2) ] / sin (A/2)

A is the angle of prism = 60° and

δ is the angle of deviation.

and we know μ = 1.5. So,

⇒ [sin ([60 + δ]/2) ] / sin (60/2) = 1.5

⇒  [sin ([60 + δ]/2) ] = 1.5 × 0.5 = 0.75

⇒ ([60 + δ]/2) = sin⁻¹ (0.75) = 48.6°

⇒ 60° + δ = 2(48.6°) = 97.2°

⇒ δ = 97.2° - 60° = 37.2°

Angle of deviation is 37.2°.

So, angle of incidence i = (A + δ)/2 = (60° + 37.2°)/2 = 48.6°

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