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

A thin rod of length \(\frac{f}{3}\) lies along the axis of a concave mirror of focal length \(f\). One end of its magnified, real image touches an end of the rod. The length of the image is:

1. \(f\)

2. \(\frac{f}{2}\)$$

3. \(2f\)

4. \(\frac{f}{4}\)$$

A thin equiconvex lens of power \(P\) is cut into three parts \(A,B,\) and \(C\) as shown in the figure. If \(P_1,P_2\) and \(P_3\) are powers of the three parts respectively, then:

A medium shows relation between \(i\) and \(r\) as shown. If the speed of light in the medium is \(nc\) then the value of \(n\) is:

A person can see clearly objects only when they lie between 50 cm and 400 cm from his eyes. In order to increase the maximum distance of distinct vision to infinity, the type and power of the correcting lens, the person has to use will be:

A boy is trying to start a fire by focusing sunlight on a piece of paper using an equiconvex lens of focal length \(10\) cm. The diameter of the sun is \(1.39\times 10^9~\text{m}\) and its mean distance from the earth is \(1.5\times 10^{11}~\text{m}.\) What is the diameter of the sun's image on the paper?
1. \( 9.2 \times 10^{-4}~\text{m} \)
2. \(6.5 \times 10^{-4}~\text{m} \)
3. \(6.5 \times 10^{-5}~\text{m} \)
4. \( 12.4 \times 10^{-4}~\text{m} \)