Question

A $4.5 \,cm$ object is placed perpendicular to the axis of a convex mirror of focal length $15 \,cm$ at a distance of $12\, cm$ . The size of the image is

• A. $6.0 \, cm$
• B. $4.5 \, cm$
• C. $3.0 \, cm$
• D. $2.5 \, cm$

Answer 1

Answer: (D)

$2.5 \, cm$

Answer 2

Here, $u = -12 \,cm, f = 15\, cm$
$\frac{1}{f} = \frac{1}{v} + \frac{1}{u}$
$\frac{1}{v} = \frac{1}{f} -\frac{1}{u}$
$\frac{1}{v} = \frac{1}{15} + \frac{1}{12}$
$\frac{1}{v} = \frac{5+4}{60}$
$v = \frac{60}{9} cm$
Now,
$\frac{I}{O} = \frac{u}{v}$
$\frac{4.5}{O} = \frac{12}{60/9 }$
Length of object
$= \frac{4.5 \times 5}{9} = 2.5 \,cm$