A glass prism of refractive index $1.5$ is immersed in water $(\mu=4/3)$. Light beam incident normally on the face $AB$ is totally reflected to reach the face $BC$ if

Given -- $\mu_{g}=1.5, \mu_{w}=4/3$

As the light beam is normal to prism surface AB, so it will enter in prism without any deviation. Same will happen with water surface. Now the beam will reach to face BC, when it gets total internal reflection from surface AC.

$\angle\theta'=\angle\theta$, because angle between two lines is equal to the angle between perpendiculars of the two lines.

We have the condition for total internal reflection,

$\sin\theta>1/_{w}\mu_{g}$

or $\sin\theta>\mu_{w}/\mu_{g}$

or $\sin\theta>(4/3)/1.5$

or $\sin\theta>8/9$