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. \(x+x' \ge 2f\)

The diameter of the eye-ball of a normal eye is about 2.5 cm. The power of the eye lens varies from:

1. 2 D to 10 D

2. 40 D to 32 D

3. 9 D to 8 D 

4. 44 D to 40 D

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 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:

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