Question

Three isosceles right angled prisms of refractive indices m₁, m₂ and m₃ are joined together so that the faces of the middle prism are in contact each with one of the outside prisms. If the ray passes through the composite block undeviated, then value of $\mu _ { 1 } ^ { 2 }$ +$\mu _ { 2 } ^ { 2 }$ is–

• A. 2
• B. 3
• C. 4
• D. 1

Answer 1

Answer: (D)

1

Answer 2

r₁ + r₂ = 90⁰

r₃ + r₄ = 90⁰

r₅ + r₆ = 90⁰

r₇ = 90⁰ – i

Use snell's law

sin i = m₁ sin r₁

m₁ sin r₂ = m₂ sin r₃

m₂ sin r₄ = m₃ sin r₅

m₃ sin r₆ = sin r₇

Using these all equation we compare $\mu _ { 1 } ^ { 2 }$ + $\mu _ { 3 } ^ { 2 }$ – $\mu _ { 2 } ^ { 2 }$ = 1