Question

An object $2cm$ high is placed at a distance of $16cm$ from a concave mirror, which produces a real image $3cm$ high. What is the focal length of the mirror?

• A. $-9.6cm$
• B. $-3.6cm$
• C. $-6.3cm$
• D. $-8.3cm$

Answer 1

Answer: (A)

Here, $h_1=2cm,u=-16cm$
$h_2=-3cm$ (since image is real and inverted)
$\because m=\frac{h_2}{h_1}=-\frac{v}{u}$
$\therefore v=\frac{-h_2}{h_1}u=\frac{3}{2}\times \left(-16\right)$
$=-24cm$
$\frac{1}{f}=\frac{1}{v}+\frac{1}{u}$
$=-\frac{1}{24}-\frac{1}{16}$
$=\frac{-2-3}{48}=\frac{-5}{48};$
$f=\frac{-48}{5}=-9.6cm$