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 $1.5$.

$A$ ray of light is incident on the hypotenuse of a right-angled prism after travelling parallel to the base inside the prism. If $\mu$ is the refractive index of the material of the prism, the maximum value of the base angle for which light is totally reflected from the hypotenuse is

$A$ light ray is incident from a denser medium to a rarer medium at an angle of incidence $i$. If the reflected and refracted rays are mutually perpendicular,then the critical angle for the interface is:

$A$ transparent cube of side $d$,made of a material of refractive index $\mu_2$,is immersed in a liquid of refractive index $\mu_1$ (where $\mu_1 < \mu_2$). $A$ ray is incident on the face $AB$ at an angle $\theta$ (as shown in the figure). Total internal reflection takes place at point $E$ on the face $BC$. The angle $\theta$ must satisfy:

The wavelength of light in two liquids $x$ and $y$ is $3500 \ \mathring{A}$ and $7000 \ \mathring{A}$ respectively. The critical angle of $x$ relative to $y$ will be.......$^o$

$A$ ray of light travelling in a transparent medium of refractive index $\mu$ falls on a surface separating the medium from air at an angle of incidence of $45^o$. For which of the following values of $\mu$ can the ray undergo total internal reflection?