Question

A pen of length 12 cm is placed at 2 cm from a ball bearing (polished) of diameter 12 cm, the image formed due to reflection by its outer part is a

• A. Virtual image of 7.2 cm length
• B. Real image of 7.2 cm length
• C. Virtual image of 20 cm length.
• D. Real image of 20 cm length.

Answer 1

The correct option is A Virtual image of 7.2 cm length

Polished surface acts like a mirror(spherical);
$\frac{1}{v}+\frac{1}{u}=\frac{1}{f}$
where,
$f=\frac{R}{2}=\frac{12}{4}=3cm$
$\frac{1}{v}+\frac{1}{(-2)}=\frac{1}{3}(given,u=-2)$
$\frac{l}{v}=\frac{1}{3}+\frac{1}{2}=\frac{2}{6}+\frac{3}{6}$
$v=1.2$

$m=\frac{-\left(v\right)}{u}$
$=\frac{-\left(1.2\right)}{-2}=0.6$
$h^{\prime }=0.6\times 12=7.2cm$
So, image is erect, virtual and 7.2 cm in length.