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One face of a prism of refractive index ...

One face of a prism of refractive index `1.5` and angle `75^(@)` is covered with a liquid of refractive index `(3sqrt(2))/(4)`. What should be the angle of incidence of light on the clear face of prism for which light is just totally refracted at the liquid covered face ?

Text Solution

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For total reflection at the liquid covered face, `i_(2) = C`, Fig.

When `sinC = (1)/(mu) = (mu_(1))/(mu_(2))`
`= (3sqrt(2)//4)/(3//2) = (2sqrt(2))/(4) = (1)/(sqrt(2)) = sin 45^(@)`
`:. C = i_(2) = 45^(@)`,
Now, `r_(1) + i_(2) = A 75^(@)`
`r_(1) = 75^(@) - i_(2) = 75^(@) - 45^(@) =30^(@)`
As `mu = (sin i_(1))/(sin r_(1))`
`:. sin i_(1) = mu sin mur_(1) = (3)/(2) sin 30^(@) = (3)/(4)`
`i_(1) = sin^(-1) (3//4) = 48.6^(@)`
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