A fish is a little away below the surface of a lake. If the critical angle is \(49^{\circ},\) then the fish could see things above the water surface within an angular range of \(\theta^{\circ}\) where:

1.	\(\theta = 49^{\circ}\)	2.	\(\theta = 90^{\circ}\)
3.	\(\theta = 98^{\circ}\)	4.	\(\theta = 24\frac{1}{2}^{\circ}\)

An object is placed at a point distance \(x\) from the focus of a convex lens and its image is formed at \(I\) as shown in the figure. The distances \(x\) and \(x'\) satisfy the relation:

          
1. \(\frac{x+x'}{2} = f\)
2. \(f = xx'\)
3. \(x+x' \le 2f\)
4. \(x+x' \ge 2f\)

On an optical bench a point object is placed at the mark of \(10\) cm, a convex lens of focal length \(15\) cm at the mark of \(40\) cm and a concave lens of focal length \(15\) cm placed at the mark of \(60\) cm. The final image is formed at the mark of: (point object and two lenses are coaxial)
1. \(30\) cm
2. \(80\) cm
3. \(90\) cm
4. infinity

Two similar plano-convex lenses are combined together in three different ways as shown in the adjoining figure. The ratio of the focal lengths in three cases will be:

1. \(2:2:1\)
2. \(1:1:1\)
3. \(1:2:2\)
4. \(2:1:1\)

A liquid of refractive index \(1.33\) is placed between two identical plano-convex lenses, with refractive index \(1.50\). Two possible arrangements, \(P\) and \(Q\), are shown. The system is:
          

A ray of light falls on a prism \(ABC\) \((AB= BC)\) and travels as shown in figure. The refractive index of the prism material should be greater than:

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 light ray is incident at an angle of \(30^{\circ}\) on a transparent surface separating two media. If the angle of refraction is \(60^{\circ}\), then the critical angle is:
1. \(\sin^{- 1} \left(\frac{1}{\sqrt{3}}\right)\)
2. \(\sin^{- 1} \left(\sqrt{3}\right)\)
3. \(\sin^{- 1} \left(\frac{2}{3}\right)\)
4. \(45^{\circ}\)