$A$ 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

For a ray of light,the critical angle is minimum,when it travels from

$A$ ray of light refracts from medium $1$ into a thin layer of medium $2$,crosses the layer,and is incident at the critical angle on the interface between medium $2$ and $3$ as shown in the figure. If the angle of incidence of the ray is $\theta$,the value of $\theta$ is

Consider telecommunication through optical fibres. Which of the following statements is not true?

$A$ ray is incident on a prism $ABC$ and travels as shown in the figure. The minimum refractive index of the material of the prism should be .......

There is a small source of light at some depth below the surface of water (refractive index $= 4/3$) in a tank of large cross-sectional surface area. Neglecting any reflection from the bottom and absorption by water,the percentage of light that emerges out of the surface is (nearly) ..........$\%$. [Use the fact that the solid angle subtended by a cone of semi-vertical angle $\theta$ is $\Omega = 2\pi(1 - \cos\theta)$]