To Find Focal Length Of A Convex Mirror Using Convex Lens - Practice Questions & MCQ

Aim-
To find the focal length of a convex mirror, using a convex lens.

Apparatus-
An optical bench with four uprights (two fixed uprights in middle, two outer uprights with lateral movement), convex lens (20 cm focal length), convex mirror, a lens holder, a mirror holder, two optical needles, (one thin, one thick) a knitting needle, and a half metre scale.

Theory-

Focal length of a convex mirror $f=\frac{R}{2}$
where R= radius of curvature of the mirror.

Experiment arrangement and ray diagram-

An auxiliary convex lens L is introduced between the convex mirror M and object needle 0 as shown in ray diagram (a). Keeping the object needle at distance about 1.5 times rough focal length of convex lens, the position of convex mirror behind convex lens is so
adjusted that a real and inverted image of object needle O, is formed at O itself.Under such condition, the light rays are incident normally over the convex mirror to retrace their path. In the absence of convex mirror, these rays would have met at centre of curvature C of the convex mirror. The distance PC gives the radius of curvature R of the mirror.

To locate the position of C, convex mirror is removed (without disturbing the object needle O and convex lens L ). An image needle I is put behind the convex lens and moved to a position at which there is no parallax between tip of inverted image of O needle and tip of I needle. Position of image needle I gives position of centre of curvature C of the mirror M ray diagram (b)

 Then PC= PI=R

and $f=\frac{R}{2}=\frac{P I}{2}$

f= focal lenght 

R= radius of curvature of mirror

Procedure-

1.    The rough focal length of the convex lens is determined by focusing a distant object.

To set the lens
2. Clamp the holder with lens in a fixed upright and keep the upright at 50 cm mark.
3. Adjust the lens such that its surface is vertical and perpendicular to the length of the optical bench.
4. Keep the upright fixed in this position throughout.

To set the object needle
5 .Take the thin optical needle as object needle (O). Mount it in outer laterally move-able upright near
zero end.
6. Move the object needle upright and clamp it at a distance (in full cm) nearly 1.5 times the obtained
rough focal length of the lens.

7. Adjust height of the object needle to make its tip lie on horizontal line through the optical centre of the lens.
8. Note the position of the index mark on the base of the object needle upright.

To set the convex mirror
9. Clamp the holder with convex mirror in second fixed upright near the lens upright, keeping reflecting
surface of the mirror towards lens.
10. Adjust the height of the mirror to make its pole lie on horizontal line through the optical centre of the
lens. 

11. Make the mirror surface vertical and perpendicular to the length of the optical bench (the principal
axes of mirror and lens must coincide.)
12. Move towards zero end of the optical bench (where object needle is mounted).
13. Closing left eye, keep open right eye about 30 cm away from the tip of the object needle.

14. See the inverted image of the object needle (formed by reflection from the convex mirror).
15. Keep the eye in a position at which the tips of the inverted image and the object needle are seen
simultaneously.
16. Adjust the height of the needle so that the two tips are seen in one line with right open eye.

17. Move the eye towards right. The tips will get separated. The tips have parallax.
18. Move the convex mirror back and forth till tip to tip parallax is removed.
19. Note the position of the index mark on the base of the convex mirror upright.

To set the image needle
20. Remove the convex mirror, keeping upright in its position.
21. With left eye closed, see with the right open eye from the other end of the optical bench. An inverted
and enlarged image of the object needle will be seen. Tip of the image must lie in the middle of the
lens.

22. Mount the thick optical needle (image needle) in the fourth upright near the other end of the optical
bench.
23. Adjust the height of the image needle so that its tip is seen in line with the tip of the image when seen
with right open eye.
24. Move the eye towards right. The tips will get separated. The image tip and the image needle tip have
parallax.

25. Remove the parallax tip to tip.
26. Note the position of the index mark on base of the image needle upright.
27. Record the position of the index marks.

To determine index correction
28. Find index correction for distance between pole of convex mirror and tip of the image needle.

To get more observations
29. Move object needle upright towards lens by 2 cm to get more observation and Repeat the experiment.
30. Move object needle upright away from lens (from position of observation 2 ) by 2 cm to get
more observation and Repeat the experiment.
31 Get more and more observations from the experiment and on the basis of observations find out the focal length of the given convex mirror.

Observations
Rough focal length of the convex lens = .....
Actual length of the knitting needle=....

 Observed distance between image needle I and back of the convex mirror

y =....

So Index correction =(x-y)=...

Calculations
1. Write down both observed PI and corrected PI 
2. Divide corrected PI by 2  to get f
3. Find mean of values of f recorded 

Result
The focal length of the given convex mirror=....cm