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The graphs given apply to a convex lens of focal length $f$ , producing a real image at a distance v from the optical center when self luminous object is at distance u from the optical center. The magnitude of magnification is m. Identify the following graphs with the first named quantity being plotted along y-axis . Assume object distance grater than focal length:
Column I Column II
p. v against u a.
q. $\frac{1}{v} a g a i n s t \frac{1}{u}$ b.
r m against v c.

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$p \to a, q \to c, r \to b$

$p \to b, q \to a, r \to c$

$p \to c, q \to b, r \to a$

$p \to b, q \to c, r \to a$

answer is D.

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Detailed Solution

$\begin{array}{l} \frac{1}{v} + \frac{1}{u} = \frac{1}{f} \\ W h e n u \to \infty, v \to f; w h e n v \to \infty, u \to f \end{array}$

$\frac{1}{v} v s \frac{1}{u}$ graph will be straight line as shown in (c)

$\frac{1}{u} + \frac{1}{f} = \frac{1}{v} \Rightarrow u = \frac{v f}{v - f}$

$| m | = \frac{v}{u} = \frac{v f}{v - f}$ ; hence, $| m |$ vs v graph will be straight line as shown in (a).

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