Page 70 - Physics - XII

1
1
The focal length of a lens can also be determined by plotting graphs between u and v or between and .
v
u
1
1
From equation (1), it is clear that the graph between and will be a straight line with negative slope.
u v
1 1 1 1 1 1 1
If = 0, then = and if = 0 then =, . Hence, the intercepts of the graph on both the axes are .
v u f u v f f
Therefore, the graph between u and v will be a hyperbola.
Equation (2) shows that the values of u and v are interchangeable
B′
L
Image of AB

A O A′
2F F F 2F C
Object needle Image needle
AB CD D
B u v

Fig. 3.3: Determination of focal length of convex lens

Procedure
1. Obtain a sharp image of the distant object such as tree, building on a white painted wall on the other
side of the lens. Measure the distance between the lens and wall (screen). This distance will give the

rough focal length of the convex lens.
2. Mount the convex lens with its holder on the central upright of the optical bench. Also, mount the two
needles on the other uprights, one on each side of the lens so that tips of the needles are at the same
height as the optical centre of the lens.
3. Measure the length of the index needle and also the distance between each needle and the lens when
held at a distance equal to length of the index needle. Find the index correction for and v.
4. Place object needle AB between f and 2f (approx. 3/2 times the rough focal length). Look on the other
side of the lens for the inverted image of the object needle at a distance more than 2f. Adjust the
position of the image needle CD till the parallax is removed tip to tip between the image needle and the
image of the object needle. Note the positions of the lens, the object needle, and the image needle on
the bench scale and fi nd the observed value of u and v.
5. Repeat the above steps for four diff erent sets of observations by placing the object needle beyond 2f
and between f and 2f.

Observations
1. Rough focal length of the lens = _____ cm
2. Actual length of the index needle = x = _____ cm
3. Observed distance between the lens and the object needle when index needle is placed between them
= y = _____ cm
4. Observed distance between the lens and the image needle when index needle is placed between them
= z = _____ cm
5. Index correction for u = (x – y) = _____ cm
6. Index correction for v = (x – z) = _____ cm

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