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 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:

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

The focal length of a glass $\left(\mu =1.5\right)$ lens in air is 20 cm. If it is dipped in water $\left(\mu =\frac{4}{3}\right)$, its focal length in water will be:

When a concave mirror of focal length f is immersed in water, its focal length becomes f', then:

Two convex lenses of focal length X and Y are placed parallel to each other. An object at infinity from the first lens forms its image at infinity from the second lens. The separation between the two lenses should be:

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

1. 15 cm

2. 30 cm

3. 35 cm

4. 45 cm

If \(C_1,~C_2 ~\mathrm{and}~C_3\) are the critical angle of glass-air interface for red, violet and yellow color, then:

An object is placed 20 cm in front of a concave mirror of a radius of curvature 10 cm. The position of the image from the pole of the mirror is:

1. 7.67 cm

2. 6.67 cm

3. 8.67 cm

4. 9.67 cm

When a ray of light falls on a given plate at an angle of incidence \(60^{\circ}\), the reflected and refracted rays are found to be normal to each other. The refractive index of the material of the plate is: