Finding the focal length of a convex lens by plotting graph between u and v

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Aim : To find the focal length of a convex lens by plotting graph between u and v.

Apparatus : An optical bench with three upright (central upright fixed , two outer uprights with lateral movements ), a convex lens with lens holder , two optical needle , (one thin , one thick ) a knitting needle and a half meter scale .

Theory : The relation between u , v and for a convex lens is

1/f= 1/v – 1/u Where f=focal length of convex lens

i/f = u-v/uv u =distance of object needle from optical center of the lens (-)

f =uv/u-v v = distance of image needle from optical from optical center of lens (+)

Procedure

  1. Mount the concave mirror in the mirror holder .
  2. Obtain the image of a tree or building outside of the window on a screen and move the mirror forward and backwards to get a sharp image on the screen .
  3. Measure the distance between mirror and screen (rough focal length ).
  4. Clamp the holder with lens fixed upright at 50cm mark .
  5. Adjust the lens so that its surface is vertical and upright keep it fixed .
  6. Take the thin optical needle as object needle (o).Mount it in outer laterally moveable upright near zero end .
  7. Move the object needle upright and clamp it at a distance nearly 1.5 times the rough focal length obtained earlier .
  8. Adjust height of the object needle to move its tip lie on a horizontal line through the optical center of the lens .
  9. Note the position of the index mark on the base of object needle .
  10. With the eye closed , see with the right eye from the other end of the optical bench . An inverted and enlarged image of the object needle will be seen .
  11. Mount the thick optical needle in the fourth upright near the other end of the optical bench .
  12. Adjust the height of the image needle (thick) so that its tip is seen in line with the tip of the image when seen with the right eye open .
  13. Move the eye towards right .The tip will get separated .The image tip and the image needle tip have parallax .
  14. Remove the parallax tip to tip .
  15. Note the position of the index mark on base of image needle .
  16. Record the position of the index mark on the base of upright of lens , the object and image needle .
  17. Find index correction (if any ) as described for distance between optical center of lens and tip of image or object needle .
  18. Move object needle upright towards mirror in steps of 1 cm to get observation .Repeat the experiment .
  19. Move object needle upright towards mirror in steps of 1 cm to get the rest of the observation . Repeat the experiment .
  20. Record your observation .

Result

F =uv /u-v f from u-v graph

Diagram

Focal length of convex lens

Convex Lenx Focal Length Diagram

Graph between u and v. It is a rectangular hyperbole.

Observation table

S No Position of lens (cm) Object length u (inch) Image lens v

(in cm)

Position of object Position of image 1/u 1/v
1 80 60 32 20 11.2 0.0107 0.0312
2 80 65 34 25 11.6 0.018 0.29
3 80 50 39.3 30 121.3 0.02 0.054
4 80 45 46 35 126 0.122 0.204
5 80 40 48 40 135 0.25 0.181

Total = 0.312 cm 0.0167cm

Calculation

1/f=1/v-1/u

=0.0312 –(0.0167)

0.0479cm

F =1/0.479

Precaution

  1. Tip of the object and image needle should lie at same height as the centre of the lens .
  2. Parallax should be removed from tip to tip.

Sources of error

  1. The upright may not be vertical .
  2. Parallax removed may not be perfect .

Viva questions

Define and give lens formula .

The equation relating the object distance (u) , the image distance (v) and lens focal length (f) is called lens formula 1/u+ 1/v = 1/f.

What are the various assumption made in deriving lens formula ?

The following assumption are made :

The lens is thin .

The lens has a small .

The point object lies on to the principal axis and placed perpendicular

The incident ray make small angles with the lens surface on the principal axis .

Which convex lens has more focal length , thick or thin ?

A convex lens has more focal length .

Define optical centre of a lens ?

It is a fixed point inside the lens on its principal axis through which light ray passing undeviated .

What is the principal axis of a lens ?

The straight line passing through the centre of curvature of the curved surfaces of the lens is the principal axis of a lens .

You can also get Class XII Practicals on BiologyPhysics, and Physical Education.


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