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The refractive index of the material of a prism of refracting angle `45^@` is `1.6` for a certain monochromatic ray. What will be the minimum angle of incidence of this ray on the prism so that no TIR takes place as the ray comes out of the prism.

Text Solution

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Given `A=74^@ ,mu=1.66`
we have
`mu=1/(sinC)` or, `sinC=1/mu=3/5`
For total internal reflection not to take place at the surface AC, we have
`r_(2) le C` or `(r_(2))=C`
Now,`r_(1)+r_(2)=A` or, `r_(1)(A-r_(2))`
or, `(r_(1))_(max)=A-(r_(2))_(max)=74^@-37^@=37^@`
For the refraction at the first face,
We have, `mu=(sini_(1))/(sinr_(1))`
or, `sini_(1)=musinr_(1)=5//3xxsin37^@`
`implies i_(1)=90^@`
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