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?

1.	\(8\) cm inside the sphere	2.	\(12\) cm inside the sphere
3.	\(4\) cm inside the sphere	4.	\(3\) cm inside the sphere

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:

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. \(2:1:1\)

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

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. \(x+x' \ge 2f\)

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:

To increase the magnifying power of a telescope: