Question

For a concave lens of focal length $f$, the relation between object and image distances $u$ and $y$, respectively, from its pole can best be represented by($u=v$ is the reference line):

• A.
• B.
• C.
• D.

Answer 1

The correct option is A

From lens formula,
$\frac{1}{v}-\frac{1}{u}=\frac{1}{f}\Rightarrow v=\frac{uf}{u+f}$

On differentiating lens formula,
$\frac{dv}{du}=\frac{v^2}{u^2}$

Case-I:
If $v=u\Rightarrow f+u=f\Rightarrow u=0$
$\frac{dv}{du}=\frac{v^2}{u^2}=1$

Case-II:
If $u=\infty$ then $v=f$
Hence, correct $u$ versus $v$ graph, that satisfies this condition is (a).