Question

An object is placed $1m$ in front of the curved surface of a plano-convex lens whose plane surface is silvered. A real image is formed in front of the lens at a distance of $120cm$. Then, the focal length of the lens is:

• A. $100cm$
• B. $120cm$
• C. $109.1cm$
• D. $110.0cm$

Answer 1

The correct option is C $109.1cm$

$u=-100cm$
$v=-120cm$
$F=?$
$\frac{1}{F}+\frac{1}{u}+\frac{1}{v}=\frac{1}{-100}+\frac{1}{-120}$
$\frac{1}{F}=-\frac{6+5}{600}=-\frac{11}{600}$
Now, $\frac{1}{F}=\frac{2}{f_1}+\frac{1}{f_m}=\frac{2}{f_1}$
or $f_1=2F$
or $f_1=2\times \frac{600}{11}$
[Negative sign is not to be used here.]
or $f_1=\frac{1200}{11}=109.1cm$.