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Calculate the angle of incidence on the ...

Calculate the angle of incidence on the face of a prism of refracting angle `60^(@)` and of refractive index 1.5, for which the emergent ray just grazes the other face.

Text Solution

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`mu = (sin theta)/(sin r_(2))`
From figure,
`1.5 = (sin 90^(@))/(sin r_(2))`
`sin r_(2) = (1)/(1.5)`
`= 0.6667`
`r_(2) = 41^(@)49'`
But `r_(1) + r_(2) = A, r_(1) = A - r_(2) = 60^(@) - 41^(@)49' = 18^(@)11'`
`mu = (sin i_(1))/(sin r_(1))`
`sin i_(1) = mu sin r_(1)`
`= 1.5 sin 18^(@)11'`
`= 1.5 xx 0.3121`
`= 0.4682`
`:. i_(1) = 27^(@)55'`
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