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

The refracting angle of a prism is `60^(@)` and its refractive index is `sqrt((7)/(3)`. What should be the minimum angle of incidence on the first refracting surface so that the ray can emerge somehow from the second refracting surface?

Text Solution

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Let I be the limiting angle of incidence, then
`sini = sqrt(mu_(2) - 1) * sinA - cosA`
`= sqrt((7)/(3) - 1) * sin60^(@) - cos60^(@)`
`(2)/(sqrt(3)) * (sqrt(3))/(2) - (1)/(2) = 1 -(1)/(2) = (1)/(2) = sin30^(@)`
`therefore " " I = 30^(@)`
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