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

If the focal length of the objective lens is increased, then magnifying power of: