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The refracting angle of a prism is 60^(@...

The refracting angle of a prism is `60^(@)` and the refractive index of its material is `sqrt((7)/(3)).` Find the minimum angle of incidence of a ray of light falling on one refracting face of the prism such that the emerging ray will graze the other refracting face.

Text Solution

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The correct Answer is:
See Section 2.9.7; and establish the relation
`i_(1) = sin^(-1) [sinAsqrt(mu^(2) - 1) - cosA]`
`"Here", " " mu = sqrt((7)/(3)) or, mu^(2) - 1 = (4)/(3)`
`or, " " sqrt(mu^(2) - 1) = sqrt((4)/(3)) = (2)/(sqrt(3))`
Given that `A = 60^(@)`
`or, " " sinA = (sqrt(3))/(2)`
`therefore " " cosA = (1)/(2)`
`"Hence", i_(1) = sin^(-1) [(sqrt(3))/(2) xx (2)/(sqrt(3)) - (1)/(2)]`
`= sin^(-1) ((1)/(2)) = 30^(@)`
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