A transparent cube of side, made of a material of refractive index $\mu $2, is immersed in a liquid of refractive index $\mu $1($\mu $1 < $\mu $2). A ray is incident on the face AB at an angle $\theta $(shown in the figure). Total internal reflection takes place at point E on the face BC. Then $\theta $ must satisfy :

Question

A transparent cube of side, made of a material of refractive index $\mu $₂, is immersed in a liquid of refractive index $\mu $₁($\mu $₁ < $\mu $₂). A ray is incident on the face AB at an angle $\theta $(shown in the figure). Total internal reflection takes place at point E on the face BC.
Then $\theta $ must satisfy :

$\theta > {\sin ^{ - 1}}\sqrt {{{\mu _2^2} \over {\mu _1^2}} - 1} $

$\theta < {\sin ^{ - 1}}\sqrt {{{\mu _2^2} \over {\mu _1^2}} - 1} $

$\theta < {\sin ^{ - 1}}{{{\mu _1}} \over {{\mu _2}}}$

$\theta > {\sin ^{ - 1}}{{{\mu _1}} \over {{\mu _2}}}$

Solution

Please login to view the detailed solution steps...

Go to DASH