If light travels a distance $x$ in time $t_1$ sec in air and $10x$ distance in time $t_2$ sec in a certain medium,then find the critical angle of the medium.

An endoscope is employed by a physician to view the internal parts of a body organ. It is based on the principle of

$A$ rod of glass $(\mu = 1.5)$ with a square cross-section is bent into the shape shown in the figure. $A$ parallel beam of light falls on the plane flat surface $A$ as shown. If $d$ is the width of a side and $R$ is the radius of the inner circular arc,what is the maximum value of $\frac{d}{R}$ such that the light entering the glass slab through surface $A$ emerges from the glass through $B$?

$A$ ray of light propagates from glass (refractive index $= 3/2$) to water (refractive index $= 4/3$). The value of the critical angle is:

What will be the minimum angle of incidence $i$ such that total internal reflection takes place at both interfaces (in $^{\circ}$)? (Given: $\mu_1 = \sqrt{2}, \mu_2 = 2, \mu_3 = \sqrt{3}$)

$A$ ray of light passes from a denser medium to a rarer medium at an angle of incidence $i$. The reflected and refracted rays make an angle of $90^{\circ}$ with each other. The angles of reflection and refraction are respectively $r$ and $r^{\prime}$. The critical angle is given by: