Page 71 - Physics - XII

Table for u, v, 1 , and 1
u v
S. Position of Observed distance Corrected distance 1 1
No. Object Lens Image u = OA v = OC u v u v
needle O needle (cm ) (cm )
–1
–1
AB (cm) CD (cm) (cm) (cm) (cm)
(cm) (cm)
1.

2.
3.
4.

Graph and Calculations

1. Graph between u and v: Choose a suitable, but the same scale to represent u along negative X-axis
(X'-axis) and v along Y-axis. According to sign convention in this case, u is negative and v is positive.

Scale used on: Y
Negative x-axis (X′-axis) : 1 cm =... cm of –u
Y-axis : 1 cm =... cm of v

v (cm)

(– 2f, 2f) P R

2f

45°
X′ Q O X
u (cm)
2f
Y′
Fig. 3.4: Graph showing relation between u and v for a convex lens

Plot the points for various sets of values of u and v from the observation table. The graph comes out to
be a rectangular hyperbola shown in Fig. 3.4.
Draw a line OP making angle of 45° with either axis OY or OX', and meeting the curve at P. The co-
ordinates of this point P are (–2f, 2f). Draw PR and PQ perpendicular on Y and X' axes respectively.

The values of magnitude of u and v will be same for point P, as we know for a convex lens, when
u = –2f, v = 2f. Hence, PQ = PR = Magnitude of 2f,

Thus, f = PQ and also f = PR
2 2
Mean value of f = _____ cm

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