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:

1.	\(X+Y\)	2.	\(\dfrac{X +Y}{2}\)
3.	\(X-Y\)	4.	\(\dfrac{X -Y}{2}\)

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

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:

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