Question

If the distances of an object and its virtual image from the focus of a convex lens of focal length f are 1 cm each, then f is

• A. $4cm$
• B. $(\sqrt{2}+1)cm$
• C. $2\sqrt{2}cm$
• D. $(2+\sqrt{2})cm$

Answer 1

The correct option is B $(\sqrt{2}+1)cm$


Here, u = – (f – 1)
v = – (f + 1)
f = + f
Applying lens formula,
$\frac{1}{v}-\frac{1}{u}=\frac{1}{f}$
$\frac{1}{-(f+1)}+\frac{1}{(f-1))}=\frac{1}{f}$
or $f^2–2f–1=0$
$f=(\sqrt{2}+1)cm$