$A$ small bulb is placed at the bottom of a tank containing water to a depth of $\sqrt{7} \; m$. The refractive index of water is $\frac{4}{3}$. The area of the surface of water through which light from the bulb can emerge out is $x \,\pi \; m^{2}$. The value of $x$ is ...............

In the figure,$ABC$ is the cross-section of a right-angled prism and $BCDE$ is the cross-section of a glass slab. The value of $\theta$ so that light incident normally on the face $AB$ does not cross the face $BC$ is (given $\sin^{-1}(3/5) = 37^o$):

With respect to air,the critical angle in a medium for light of red colour $[{\lambda _1}]$ is $\theta$. Other factors remaining the same,the critical angle for light of yellow colour $[{\lambda _2}]$ will be:

In the diagram shown,a ray of light is incident on the interface between medium $1$ and $2$ at an angle slightly greater than the critical angle. The light undergoes total internal reflection at this interface. After that,the light ray falls on the interface of medium $1$ and $3$,and again it undergoes total internal reflection. Which of the following relations should hold true?

When a rectangular metal tank is filled to the top with an unknown liquid,an observer with eyes level with the top of the tank can just see the corner $E$. $A$ light ray that refracts towards the observer at the top surface of the liquid is shown. The refractive index of the liquid is:

$A$ rectangular glass block is placed on a printed paper lying on a horizontal surface. Find the minimum refractive index of the glass for which the letters on the paper are not visible from any of the vertical sides of the block.