$A$ ray of light is incident on one face of a $90^{\circ}$ prism and undergoes total internal reflection at the glass-air interface. If the angle of incidence is $45^{\circ}$,then the refractive index $n$ is:

Consider light travelling from a medium $A$ to medium $B$ separated by a plane interface. If the light undergoes total internal reflection during its travel from medium $A$ to $B$ and the speed of light in media $A$ and $B$ are $2.4 \times 10^8 \ m/s$ and $2.7 \times 10^8 \ m/s$ respectively, then the value of critical angle is:

The refractive indices of the material of the prism and the liquid are $1.56$ and $1.32$ respectively. Find the value of $\theta$ for total internal reflection at the interface.

$A$ wide slab consisting of two media of refractive indices $n_1$ and $n_2$ is placed in air as shown in the figure. $A$ ray of light is incident from medium $n_1$ to $n_2$ at an angle $\theta$,where $\sin \theta$ is slightly larger than $1/n_1$. Take the refractive index of air as $1$. Which of the following statement$(s)$ is(are) correct?
$(A)$ The light ray enters air if $n_2 = n_1$
$(B)$ The light ray is finally reflected back into the medium of refractive index $n_1$ if $n_2 < n_1$
$(C)$ The light ray is finally reflected back into the medium of refractive index $n_1$ if $n_2 > n_1$
$(D)$ The light ray is reflected back into the medium of refractive index $n_1$ if $n_2 = 1$

For total internal reflection to take place,the angle of incidence $i$ and the refractive index $\mu$ of the medium must satisfy the inequality

Consider a glass cube slab of dielectric bound by the planes $x=0, x=a$; $y=0, y=b$; $z=0, z=c$; with $b > a > c$. The slab is placed in air and has a refractive index of $n$. The minimum value for $n$,such that all rays entering the dielectric at $y=0$ reach $y=b$ is