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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22 Replies to “Finding the focal length of a convex lens by plotting graph between u and v”

  1. brother, there is a mistake in ur procedure.
    as the topic is based on a convex lens.
    but ur first line of ur procedure is telling about the concave lens.
    plz, try to correct it.

  2. aim is covex lens ,procedure starts with concave mirror don’t no to print or don’t no to calculate v value what an rubbish

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