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Question
How is the critical angle related to the refractive index of a medium?
Solution
The relationship is `""_amu_m = 1/sin C`
When a light beam enters a liquid (m) from point A, it becomes ∠i = C with normal and emerges from the liquid in medium air, which is rarer, producing ∠r = 90°, or the ray BO becoming parallel to the liquid surface.
∴ `""_mmu_a = sin i/sin r = sin C/(sin 90°)`
Or `""_amu_m = (sin 90°)/sin C = 1/sin C`
∴ `""_amu_m = "R.I of medium" = 1/sin C`
RELATED QUESTIONS
Explain the term critical angle with the aid of a labelled diagram.
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Copy the diagram given below and complete the path of the light ray PQ, as it emerges out of the prism by necessary angles. The critical angle of glass is 42°:
