Question

An object of height $h_1=2cm$ is placed perpendicular to the principal axis of a concave mirror of focal length 10cm. The distance of the object from the mirror is 15cm. Find the nature, position and size of the image respectively.

• A. Real, inverted v=-30cm, $h_2=-4cm$
• B. Virtual and inverted, v=6cm, $h_2=0.8cm$
• C. Real and inverted, v=30cm, $h_2=-8cm$
• D. None of the above

Answer 1

The correct option is A

Real, inverted v=-30cm, $h_2=-4cm$

Given, height of object, $h_1=2.0cm$

Focal length of convex mirror, f= -10cm.

Object distance, u=-15cm.

Image distance, v=?

Image size, $h_2=?$

according to formula,

$\frac{1}{f}$$=$$\frac{1}{v}$$+$$\frac{1}{u}$

$\frac{1}{(-10)}$$=$$\frac{1}{v}$$+$$\frac{1}{(-15)}$

$\frac{1}{v}$$=$$\frac{1}{(-10)}$$+$$\frac{1}{15}$

$\frac{1}{v}$$=$$\frac{-1}{30}$

$\frac{1}{v}$$=$$\frac{-1}{30}$

$v=-30cm$

$\frac{h_2}{h_1}=-\frac{v}{u}$

$h_2=(-2)\times \frac{(-30)}{(-15)}$

=-4cm