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

Explanation

For total reflection at the liquid covered face, `i_2 = C`,
When `sin C = (1)/(mu) = (mu_1)/(mu_2)`
=`(3 sqrt(2//4))/(3//2) = (2 sqrt(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 r_1 = (3)/(2) sin 30^@ = (3)/(4)`
`i_1 = sin^-1(3//4) = 48.6^@`.
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