What is the least radius through which an optical fiber of core diameter $0.05 \, mm$ may be bent (as shown in figure) without serious loss of light (in $, mm$)? The refractive index of the core is $1.6$ and that of cladding is $1.5$.

Write the definition of critical angle.

$A$ ray of light travels from a denser medium $(\mu)$ to air. The angle of incidence is denoted by $i$ and the angle of deviation by $D$. Let $C = \sin^{-1}(1/\mu)$. Which of the following graphs is correct?

Assertion: The refractive index of diamond is $\sqrt{6}$ and that of liquid is $\sqrt{3}$. If the light travels from diamond to the liquid,it will be totally internally reflected when the angle of incidence is $30^{\circ}$.
Reason: $\mu = \frac{1}{\sin C}$,where $\mu$ is the refractive index of diamond with respect to the liquid.

$A$ cylindrical transparent rod of refractive index $\mu = \frac{2}{\sqrt{3}}$ is surrounded by air. $A$ light ray is incident at the midpoint of one end of the rod as shown in the figure. The angle of incidence $\theta$ for which the light ray undergoes total internal reflection at the side wall of the rod is:

The critical angle for light traveling from medium $(i)$ to medium $(ii)$ is $\theta$. If the speed of light in medium $(i)$ is $v$,then the speed of light in medium $(ii)$ is: