For the angle of minimum deviation of a prism to be equal to its refracting angle, the prism must be made of a material whose refractive index:

1.	lies between \(2\) and \(\sqrt{2}\)
2.	is less than \(1\)
3.	is greater than \(2\)
4.	lies between \(\sqrt{2}\) and \(1\)

A rod of length \(10~\text{cm}\) lies along the principal axis of a concave mirror of focal length \(10~\text{cm}\) in such a way that its end closer to the pole is \(20~\text{cm}\) away from the mirror. The length of the image is:
1. \(15~\text{cm}\) 
2. \(2.5~\text{cm}\)
3. \(5~\text{cm}\)
4. \(10~\text{cm}\)

A thin prism of angle \(15^\circ\) made of glass of refractive index \(\mu_1=1.5\) is combined with another prism of the glass of refractive index \(\mu_1=1.75.\) The combination of the prism produced dispersion without deviation. The angle of the second prism should be:
1. \(5^\circ\)
2. \(7^\circ\)
3. \(10^\circ\)
4. \(12^\circ\)

A converging beam of rays is incident on a diverging lens. Having passed through the lens the rays intersect at a point \(15~\text{cm}\) from the lens on the opposite side. If the lens is removed the point where the rays meet will move \(5~\text{cm}\) closer to the lens. The focal length of the lens is:
1.  \(5~\text{cm}\)
2. \(-10~\text{cm}\)
3. \(20~\text{cm}\)
4. \(-30~\text{cm}\)

The speed of light in media \(M_1\) and \(M_2\) is \(1.5\times10^{8}\) m/s and \(2.0\times10^{8}\) m/s respectively. A ray of light enters from medium  \(M_1\) and \(M_2\) at an incidence angle \(i.\) If the ray suffers total internal reflection, the value of \(i\) is:

A ray of light is incident on a \(60^\circ\) prism at the minimum deviation position. The angle of refraction at the first face (i.e. incident face) of the prism is:
1. \(30^\circ\)
2. \(45^\circ\)
3. \(60^\circ\)
4. zero

A rainbow is formed due to:

A plane convex lens (µ = 1.5) has a radius of curvature \(10~\mathrm{cm}\). It is silvered on its plane surface. The focal length of the lens after silvering is:

1. 10 cm

2. 20 cm

3. 15 cm

4. 25 cm

Light enters at an angle of incidence in a transparent rod of refractive index n. For what value of the refractive index of the material of the rod, will the light, once entered into it, not leave it through its lateral face whatsoever be the value of the angle of incidence?
1. $n$ $>\sqrt{2}$
2. 1.0
3. 1.3
4. 1.4

A tall man, of height \(6\) feet, wants to see his full image. The required minimum length of the mirror will be: