First slide

The lens

Question

The figure shows different graphs in case of a thin convex lens for the formation of a real image, u and v are the object and image distances respectively. Find out the correct identification for the different combinations from the following.

Moderate

A

graph I, if x is v and y is u/v
B

graph II, if x is u and y is v
C

graph III, if x is v and y is u/v
D

graph IV, if x is 1/u and y is 1/v.

Solution

when real image is formed by a convex lens then lens equation will be $\frac{1}{u} + \frac{1}{v} = \frac{1}{f}$
$∴ \frac{v}{u} + 1 = \frac{v}{f}$
$∴ \frac{1}{y} + 1 = \frac{x}{f}$ graph cannot be a straight line
$∴$ Option (1) is not correct. Graph II has increase in u increase v which is not correct.
Eq. $\frac{v}{u} + 1 = \frac{v}{f}$ gives $1 + y = \frac{x}{f}$
$∴$ Linear graph (III) is not correct
$∴$ $\frac{1}{u} + \frac{1}{v} = \frac{1}{f}$ gives graph IV, Hence, option (4) is correct.

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