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

Focal length of objective lens and eyepiece of an astronomical telescope are 200 cm and 10 cm respectively. The length of telescope for maximum magnification is nearly:

1. 207 cm

2. 210 cm

3. 204 cm

4. 220 cm

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 glass sphere $\left(\mu =\frac{3}{2}\right)$ of radius 12 cm has a small mark at a distance of 3 cm from its centre. Where will this mark appear when it is viewed from the side nearest to the mark along the line joining the centre and the mark?

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. \(\theta = 98^{\circ}\)$\mathrm{}$
4. \(\theta = 24\frac{1}{2}^{\circ}\)$$

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