A liquid of refractive index \(\frac{4}{3}\) is placed between two identical planoconvex-lenses touching each other at their spherical surfaces of radius \(R\). If the refractive index of the lens is \(1.50\), then the lens behaves as:

1.	a convergent with power \(P=\frac{1}{3 R}\)
2.	a convergent with power \(P=\frac{1}{6 R}\)
3.	a divergent with power \(P=\frac{1}{3 R}\)
4.	a divergent with power \(P=\frac{1}{6 R}\)

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

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

The angle of minimum deviation for a glass prism of refractive index \(\mu = \sqrt{3}\) equals the refracting angle of the prism. The angle of the prism is:
1. \(30^{\circ}\)
2. \(60^{\circ}\)
3. \(90^{\circ}\)
4. \(45^{\circ}\)$$