Imagine that a beam of monochromatic light originates in air and is allowed to shine upon the flat surface of a piece of glass at an angle of $60°$ with the normal. The reflected and refracted beams are perpendicular to each other. What is the index of refraction of the glass?

1.  $\frac{\sqrt{3}}{3}$

2.  1

3.  2

4.  $\sqrt{3}$

The refractive index of the material of a prism is $\sqrt{2}$ and the angle of the prism is 30°. One of the two refracting surfaces of the prism is made a mirror inwards, by a silver coating. A beam of monochromatic light entering the prism from the other face will retrace its path (after reflection from the silvered surface) if the angle of incidence on the prism is:-

$1. 60°$
$2. 45°$
$3. 30°$
$4. \mathrm{Zero}$

An object is placed at a distance of 40 cm from a concave mirror of focal length 15 cm. If the object is displaced through a distance of 20 cm towards the mirror, the displacement of the image will be:-

1. 30 cm away from the mirror

2. 36 cm away from the mirror

3. 30 cm towards the mirror

4. 36 cm towards the mirror

A beam of light from a source L is incident normally on a plane mirror fixed at a certain distance x from the source. The beam is reflected back as a spot on a scale placed just above the source L. When the mirror is rotated through a small angle $\theta$, the spot of the light is found to move through a distance y on the scale. The angle $\theta$ is given by:-

1. $\frac{y}{x}$

2. $\frac{x}{2y}$

3. $\frac{x}{y}$

4. $\frac{y}{2x}$

Two identical glass ( ${\mu }_g$= 3/2) equiconvex lenses of focal length f each are kept in contact. The space between the two lenses is filled with water ( ${\mu }_w$ = 4/3). The focal length of the combination is :

1.  f/3

2.  f

3.  $\frac{4f}{3}$

4.  $\frac{3\mathrm{f}}{4}$

An air bubble in a glass slab with refractive index 1.5 (near-normal incidence) is 5 cm deep when viewed from one surface and 3 cm deep when viewed from the opposite face. The thickness (in cm) of the slab 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

1.  convex, +2.25 diopter

2.  concave, -0.25 diopter

3.  concave -0.2 diopter

4.  convex, +0.5 diopter