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 $1.5$.

$A$ fish looking up through the water sees the outside world contained in a circular horizon. If the refractive index of water is $\frac{4}{3}$ and the fish is $12 \, cm$ below the surface,the radius of this circle in $cm$ is

$A$ ray of light travelling in a transparent medium falls on a surface separating the medium from air at an angle of incidence of $45^\circ$. The ray undergoes total internal reflection. If $n$ is the refractive index of the medium with respect to air,select the possible value$(s)$ of $n$ from the following:

Total internal reflection of a ray of light is possible when the ($i_c$ = critical angle,$i$ = angle of incidence)

In the figure shown,for an angle of incidence $45^{\circ}$ at the top surface,what is the minimum refractive index $\mu$ needed for total internal reflection at the vertical face?

$A$ transparent solid cylindrical rod has a refractive index of $\frac{2}{\sqrt{3}}$. It is surrounded by air. $A$ light ray is incident at the mid-point of one end of the rod as shown in the figure. The incident angle $\theta$ for which the light ray grazes along the wall of the rod is