Question

The image of a small electric bulb fixed on the wall of a room is to be obtained on the opposite wall $4m$ away by means of a large convex lens. The maximum possible focal length of the lens required for this purpose will be

• A. 0.5 m
• B. 1.0 m
• C. 1.5 m
• D. 2.0 m

Answer 1

Answer: (B)

Let a large convex lens is placed between two walls at a distance $x$ from the wall on which an electric bulb is fixed.
Using
$\frac{1}{f}=\frac{1}{v}-\frac{1}{u}$
$=\frac{1}{4-x}-\frac{1}{-x}\left(\because u=-x,v=4-x\right)$
$=\frac{x+4-x}{\left(4-x\right)\left(x\right)}$
$=\frac{4}{(4-x)(x)}$
or $f=\frac{\left(4-x\right)x}{4}\dots \dots \left(i\right)$
Now magnification $m=\frac{v}{u}=\frac{4-x}{x}$
$⟹1=\frac{4-x}{x}$
$⟹x=4-x$
$⟹2x=4$
$⟹x=2m$
From eq. (i)
$f=\frac{(4-2)(2)}{4}=\frac{2\times 2}{4}=1m$