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)

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$