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 there is no emergent light through a prism of refracting angle \(60^{\circ},\) whatever may be the angle of incidence, then the minimum value of the refractive index of the material of the prism is:
1. \(2\)
2. \(\sqrt{2}\)
3. \(1.5\)
4. \(\sqrt{3}\)

The minimum magnifying power of an astronomical telescope is \(40\). If the length of the telescope is \(205\) cm, then the focal length of its field lens is:
1. \(5\) cm
2. \(200\) cm
3. \(40\) cm
4. \(140\) 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 astronomical telescope has angular magnification of \(40\) in its normal adjustment. If focal length of eyepiece is \(5\) cm, the length of the telescope is:
1. \(190\) cm
2. \(200\) cm
3. \(205\) cm
4. \(210\) cm

The condition of minimum deviation is achieved in an equilateral prism kept on the prism table of a spectrometer. If the angle of incidence is \(50^{\circ}\), the angle of deviation is:
1. \(25^{\circ}\)$$

2. \(40^{\circ}\)$$

3. \(50^{\circ}\)$$

4. \(60^{\circ}\)$$

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