$A$ 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 the refractive index of water is $\frac{4}{3}$ and that of a given glass slab immersed in it is $\frac{5}{3}$,the value of the critical angle for a ray of light tending to go from glass to water is:

Consider a glass prism immersed in a liquid as shown below. The refractive index of glass and liquid is $1.5$ and $1.2$, respectively. $A$ ray of light enters the prism perpendicular to the face $AB$. If the ray is totally internally reflected at the face $AC$, then the largest value of angle $\theta$ is:

It is found that electromagnetic signals sent inside a glass sphere from $A$ towards $B$ reach point $C$. The speed of electromagnetic signals in glass cannot be:

There is a small source of light at some depth below the surface of water (refractive index $= 4/3$) in a tank of large cross-sectional surface area. Neglecting any reflection from the bottom and absorption by water,the percentage of light that emerges out of the surface is (nearly) ..........$\%$. [Use the fact that the solid angle subtended by a cone of semi-vertical angle $\theta$ is $\Omega = 2\pi(1 - \cos\theta)$]

$A$ small bulb is placed at the bottom of a tank containing water to a depth of $\sqrt{7} \; m$. The refractive index of water is $\frac{4}{3}$. The area of the surface of water through which light from the bulb can emerge out is $x \,\pi \; m^{2}$. The value of $x$ is ...............