A light ray incident along vector 2 i ^ + 4 j ^ + 5 k ^ strikes on the x − z plane from medium-I of refractive index 2 and enters into medium-II of refractive index μ 2 . The value of μ 2 for

Question

A light ray incident along vector 2 i ^ + 4 j ^ ​ + 5 ​ k ^ strikes on the x − z plane from medium-I of refractive index 2 and enters into medium-II of refractive index μ 2 ​ . The value of μ 2 ​ for which the ray is just totally reflected from the boundary, is:

TestHub · Accepted Answer

μ 1 ​ sin i = μ 2 ​ sin 9 0 ∘ ​ tani = ( 2 i ^ + 4 j ^ ​ + 5 ​ k ^ ) ⋅ j ^ ​ = 25 ​ cos i ^ ( 2 2 + ( 5 ​ ) 2 ) ​ ​ ​ ​ ​ ​ cos i ^ = 5 4 ​ ; sin i ^ = 5 3 ​ ⇒ μ 2 ​ = 5 6 ​ 2 × 5 3 ​ = μ sin 9 0 ∘ μ = 5 6 ​

Physics - Geometrical Optics Question with Solution | TestHub

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