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

$A$ point source $S$ is placed at the bottom of a transparent block of height $h = 10 \ mm$ and refractive index $n_B = 2.72$. It is immersed in a liquid of lower refractive index $n_L$ as shown in the figure. It is found that the light emerging from the block into the liquid forms a circular bright spot of diameter $D = 11.54 \ mm$ on the top surface of the block. The refractive index of the liquid $n_L$ is:

For the given incident ray as shown in the figure,what is the minimum refractive index of the prism required for total internal reflection of this ray?

$A$ water-proof laser pointer of length $10 \,cm$ is placed in a water tank. It rotates about a horizontal axis passing through its centre of mass in a vertical plane as shown in the figure. The time period of rotation is $60 \,s$. Assuming the water to be still and no reflections from the surface of the tank, the duration for which the light beam escapes the tank in one time period is close to ............. $s$. (Take, refractive index of water $= 1.33$)

$A$ ray of light is incident at an angle $i$ from a denser to a rarer medium. The reflected and the refracted rays are mutually perpendicular. The angle of reflection is $r$ and the angle of refraction is $r'$. Then the critical angle $C$ will be:

In an optical fibre,the refractive index of the inner part (core) is $1.68$ and the refractive index of the outer part (cladding) is $1.44$. The numerical aperture of the fibre is ........