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Question
A transparent solid cylindrical rod has a refractive index of 2/`sqrt3`. It is surrounded by air. A light ray is incident at the mid point of one end of the rod as shown in the figure.
The incident angle θ for which the light ray grazes along the wall of the rod is ______.
Options
`sin^-1(1/2)`
`sin^-1(sqrt3/2)`
`sin^-1(2/sqrt3)`
`sin^-1(1/sqrt3)`
Solution
A transparent solid cylindrical rod has a refractive index of 2/`sqrt3`. It is surrounded by air. A light ray is incident at the mid point of one end of the rod as shown in the figure.
The incident angle θ for which the light ray grazes along the wall of the rod is `underlinebb(sin^-1(1/sqrt3))`.
Explanation:
sinC = `sqrt3/2` ...(1)
sin r = sin(90 - C) = cos C = `1/2`
`sintheta/sin"r"=mu_2/mu_1`
sinθ = `2/sqrt3xx1/2`
θ = sin-1 `(1/sqrt3)`
