$A$ ray of light from a denser medium strikes a rarer medium. The angle of reflection is $r$ and that of refraction is $r'$. The reflected and refracted rays make an angle of $90^{\circ}$ with each other. The critical angle will be

At the interface between two materials having refractive indices $n_1$ and $n_2$,the critical angle for reflection of an electromagnetic wave is $\theta_{1C}$. The $n_2$ material is replaced by another material having refractive index $n_3$,such that the critical angle at the interface between $n_1$ and $n_3$ materials is $\theta_{2C}$. If $n_3 > n_2 > n_1$,$\frac{n_2}{n_3} = \frac{2}{5}$,and $\sin \theta_{2C} - \sin \theta_{1C} = \frac{1}{2}$,then $\theta_{1C}$ is:

$A$ beam containing red,green,and blue light is incident on a prism. Their refractive indices are $1.39, 1.44$,and $1.47$ respectively. Then,the prism:

Optical fibres are related with

The critical angle of light passing from glass to air is minimum for which color of light?

$A$ 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