A transparent cube of side $d$, 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 an incident on the face $AB$ at an angle $\theta$ (shown in the figure). Total internal reflection takes place at the point $E$ on the face $BC\mathit{.}$



Then, $\theta$ must satisfy

A ray of light originates from inside a glass slab and is incident on its inner surface at an angle $\mathrm{\theta }$ as shown,

In this experiment the location $x$ of the spot where they ray hits the screen is recorded. Which of the following correctly shown the plot of variation of $x$ with the angle $\mathrm{\theta }$ ?

A $45°-90°$ prism as shown in the figure is immersed in water. A ray of light is incident normally on one of its shorter faces. The minimum index of refraction that the prism must have if this ray is to be totally reflected within the glass at the long face of the glass is (Assume refractive index of water $n_{\mathrm{water}}=1.3$)