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Question
A beam of light consisting of red, green and blue is incident on a right-angled prism as shown in figure. The refractive index of the material of the prism for the above red, green and blue colours are 1.39, 1.44 and 1.47 respectively. What are the colours suffer total internal reflection?
Solution
i > c ∴ i = 45°
`mu = 1/(sin "c")`
sin c = `1/mu`
- Red-
`"C"_"R" = sin^-1 (1/mu)`
`= sin^-1 (1/1.39)`
CR ≈ 46°
i = 45°
i < CR
- Green-
`"C"_"G" = sin^-1 (1/mu)`
`= sin^-1 (1/1.44)`
CG ≈ 44°
i = 45°
i > CG
- Blue-
`"C"_"B" = sin^-1 (1/mu)`
`= sin^-1 (1/1.47)`
CG ≈ 43°
i = 45°
i > CB
Green and blue suffer total internal reflection.
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