A ray enters at grazing incidence an assembly of three isosceles right-angled prisms with refractive indices μ₁ = √2, μ₂ = √x and μ₃ = √3. It also emerges at grazing incidence. Determine x. [See Image.]
Physics · Mixed Chapter
JEE Main Practice

Question

A ray enters at grazing incidence an assembly of three isosceles right-angled prisms with refractive indices μ₁ = √2, μ₂ = √x and μ₃ = √3. It also emerges at grazing incidence. Determine x. [See Image.]

Physics · Mixed Chapter

G1 Physics · Accepted Answer

Step 1 — For grazing incidence in the first prism μ₁ = √2, Snell law fixes refracted angle sin r₁ = 1/√2, so r₁ = 45°. Step 2 — Use isosceles-right prism geometry to trace rays across the first internal boundary and middle prism μ₂ = √x. Step 3 — For grazing emergence from last prism μ₃ = √3, the final internal incidence satisfies sin r₃ = 1/√3. Step 4 — Apply Snell law at each internal interface using interface normals in original figure. The result is x = 3. QUALITY FLAG — Exact optical ray g…