A medium shows relation between \(i\) and \(r\) as shown. If the speed of light in the medium is \(nc\) then the value of \(n\) is:

In the figure shown the angle made by the light ray with the normal in the medium of refractive index \(\sqrt{2}\) is:
                   
1. \(30^{\circ}\)$$

2. \(60^{\circ}\)$$

3. \(90^{\circ}\)$$

4. None of these

A plane mirror is placed at the bottom of a fish tank filled with water of refractive index \(\dfrac{4}{3}.\) The fish is at a height \(10~\text{cm}\) above the plane mirror. An observer \(O\) is vertically above the fish outside the water. The apparent distance between the fish and its image is:

A fish at a depth \(y\) inside the water is seeing a bird. The bird is at a height \(x\) above the water level. If the refractive index of water is \(\mu,\) then the apparent distance of bird as seen by the fish is:
1. \(x+\mu y\)
2. \(y+\mu x\)
3. \(x+\frac{y}{\mu}\)
4. \(y+\frac{x}{\mu}\)

A diverging beam of light from a point source \(S\) having divergence angle \(\alpha,\) falls symmetrically on a glass slab as shown. The angles of incidence of the two extreme rays are equal. If the thickness of the glass slab is \(t\) and the refractive index \(n\), then the divergence angle of the emergent beam is: