The phenomenon of total internal reflection is observed when the angle of incidence is

$A$ spider and a fly are on opposite sides of the surface of a glass sphere. What is the maximum solid angle $\Omega$ within which the fly can be seen by the spider?
Given: The dimensions of the spider and the fly are very small with respect to the sphere. The refractive index of the glass is $\mu_g = \sqrt{2}$.

$A$ point source of light is placed at the bottom of a vessel,which is filled with water of refractive index $\mu$ to a height $h$. If a floating opaque disc has to be placed exactly above it so that the source is invisible from above,the radius of the disc should be:

Three transparent media of refractive indices $\mu_1, \mu_2, \mu_3$,respectively,are stacked as shown below. $A$ ray of light follows the path shown. No light enters the third medium. Then,

$A$ material is embedded between two glass plates. The refractive index $n$ of the material varies with thickness as shown in the figure. The maximum incident angle (in degrees) on the material for which the beam will pass through the material is

$A$ cut diamond sparkles because of its