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

White light is incident on the interface of glass and air as shown in the figure. If green light is just totally internally reflected then the emerging ray air contains.

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

The graph shows how the magnification $m$, produced by a convex thin lens, varies with the image distance $v$. What is the focal length?