find the focal length of given convex lens by plotting graphs between u and v
Answers
Answer:
Explanation:
Objective:
To find the focal length of a convex lens by plotting graphs between u and v and between 1/u
amd 1/v.
Apparatus:
An optical bench with three uprights (central fixed, two outer uprights with lateral movement), a
convex lens with lens holder, two optical needles and a half meter scale.
Precautions:
1. Tips of the object and image needles should lie at the same height as the centre of the
lens.
2. Parallax should be removed from tip to tip by keeping eye at a distance at least 30 cm
away from the needle.
3. The object needle should be placed at such a distance that only real, inverted image of it
is formed.
4. Index correction for u and v should be applied.
Ray diagram:
Theory:
The relation between u, v and f for a convex lens is:
f v u
1 1 1
Where, f = focal length of convex lens.
u = distance of object needle from lens.
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v = distance of image needle from lens.
Note: According to sign-convention, u has negative value and v has positive value for convex
les. Hence, f comes positive.
Procedure:
1. Mount object needle, lens and image needle uprights on the optical bench.
2. Tip of the object needle, image needle and optical centre of lens must be in straight line
parallel to optical bench.
3. Place the object needle on left side of lens so as to get its inverted image of it.
4. Now place image needle on right side of lens and remove the parallax between image of
object and image needle.
5. Note down the position of object needle, lens and image needle in table.
6. For more reading move object needle slightly and again remove parallax between image
of object needle and image needle keeping lens position fixed and note down the
positions of object needle, image needle and lens.
7. In this way take at least five readings.
Calculations:
Calculations of focal length by graphical methods.
1) u-v Graph. Select a suitable but the same scale to represent u along X-axis and v along
Y-axis. According to sign conventions, in this case, u is negative and v is positive. Plot
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the various points for different sets of values of u and v from observation table. The
graph comes out to be a rectangular hyperbola as shown in figure:
Draw a line OA making an angle 450
with either axis (i.e., bisecting YOX') and
meeting the curve a point A. Draw AB and AC perpendicular on X’ and Y axis
respectively.
The values of u and v will be same for point A. So the coordinates of Point A must be (-
2f, 2f), because for a convex lens, when u =-2f, v=2f.
Hence, |OB| =|OC| =2f or OC=2f, OB=-2f
2
OB f and also
2
OC f
Mean value of f = …… cm
From Lens formula applied at point A
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f u v
1 1 1
As u =- v,
f u
1 2
or
v
2
and
2
u
f or
2
v
Hence , half the value of either coordinate of A (i.e., distance OB) gives the focal length
of the convex lens.
cm
OB f ........
2
Mean value of f = - …… cm
2)
u
1
and
v
1
Graph Select a suitable but the same scale to represent
u
1
along X’-axis and
v
1
along Y-axis. By sign conventions
u
1
is negative and
v
1
is positive. Plot the various
points for different sets of values of
u
1
and
v
1
from the observation table. The graph
comes out to be a straight line as shown in Figure
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3) The straight line cuts the two axes OX’ and OY at an angle of 450
at points P and Q
respectively and making equal interepts on the aces. Measure the distance OP and OQ.
Then focal length,
OP OQ
f
1 1
= ……cm
From the mirror formula,
f u v
1 1 1
(a) If then
u
0,
1
v f
1 1
Thus, intercept OQ =
v f
1 1
(b) If then
v
0,
1
u f
1 1
Thus, intercept OP =
u f
1 1
Result:
The focal length of the given convex lens as determined from:
(u-v) graph = ………cm
u v
1 1
graph = …………cm
Calculations = …………..cm
Sources of error:
1. The uprights may not be the vertical.
2. Parallax removal may not be perfect.