A point source of light B is placed at a distance L in front of the centre of a mirror of width d hung vertically on a wall. A man walks in front of the mirror along a line parallel to the mirror at a distance 2L from it as shown. The greatest distance over which he can see the image of the light source in the mirror is:
                       
1. d/2                                     

2. d

3. 2d                                       

4. 3d

The focal length of the objective lens and the eye lens is 4 mm and 25 mm respectively in a compound microscope. The distance between objective and eyepiece lens is 16 cm. Find its magnifying power for relaxed eye position:

1. 32.75                                 

2. 327.5 

3. 0.3275                               

4. None of the above

A medium shows relation between i and r as shown. If the speed of light in the medium is nc then the value of n is:

1. 1.5

2. 2

3.  2^–1

4. 3^–1/2

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 D

2. concave, - 0.25 D

3. concave, - 0.2 D

4. convex, + 0.15 D

In an astronomical telescope in normal adjustment a straight black line of length L is drawn on inside part of the objective lens. The eye-piece forms a real image of this line. The length of this image is l. The magnification of the telescope is:
1. L/l+1
2. L/l-1
3. L+1/L-1
4. L/l

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

A converging beam of rays is incident on a diverging lens. Having passed through the lens the rays intersect at a point 15 cm from the lens on the opposite side. If the lens is removed the point where the rays meet will move 5cm closer to the lens. The focal length of the lens is:

1. -10 cm                                   

2. 20 cm

3. -30 cm                                   

4. 5 cm

The speed of light in media ${\mathrm{M}}_1$ and ${\mathrm{M}}_2$ is $1.5\times {10}^8 \mathrm{m}/\mathrm{s}$ and $2.0\times {10}^8 \mathrm{m}/\mathrm{s}$ respectively. A ray of light enters from medium ${\mathrm{M}}_1$ to ${\mathrm{M}}_2$ at an incidence angle i. If the ray suffers total internal reflection, the value of i is:

1. equal to ${\sin }^{-1}\left(\frac{2}{3}\right)$

2. equal to or less than ${\sin }^{-1}\left(\frac{3}{5}\right)$

3. equal to or greater than ${\sin }^{-1}\left(\frac{3}{4}\right)$

4. less than ${\sin }^{-1}\left(\frac{2}{3}\right)$

A boy is trying to start a fire by focusing sunlight on a piece of paper using an equiconvex lens of focal length 10 cm. The diameter of the sun is 1.39 $\times {10}^9 m$ and its mean distance from the earth is $1.5\times {10}^{11} m$. What is the diameter of the sun's image on the paper?

1. $9.2\times {10}^{-4 }m$

2. $6.5 \times {10}^{-4 }m$

3. $6.5\times {10}^{-\mathrm{5 }}m$

4. $12.4\times {10}^{-4} m$

Two convex lenses of focal lengths 10 cm and 30 cm are kept at a separation of 20 cm. Then the correct statement is:

1. the effective focal length is 15 cm

2. chromatic aberration is minimized

3. combination behaves like a convergent lens

4. All of these