$A$ light ray falls on a square glass slab as shown in the diagram. The index of refraction of the glass,if total internal reflection is to occur at the vertical face,is equal to

If light travels a distance $x$ in time $t_1$ sec in air and $10x$ distance in time $t_2$ sec in a certain medium,then find the critical angle of the medium.

$A$ cut diamond sparkles because of its

$A$ small bulb is placed at the bottom of a tank containing water to a depth of $80 \; cm$. What is the area (in $m^2$) of the surface of water through which light from the bulb can emerge out? Refractive index of water is $1.33$. (Consider the bulb to be a point source.)

Initially,$AB$ is the interface of a slab of refractive index $\mu$ and air. $A$ ray of light strikes $AB$ at the critical angle $\theta_c$. Now,a slab $ABCD$ of refractive index $\mu_1$ is placed on top such that total internal reflection takes place at the surface $CD$ (and not at the surface $AB$). What should be the value of $\mu_1$?

$A$ 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 $n_2 = 1$