Question

A 4 cm tall object is placed perpendicular to the principal axis of a convex lens of focal length 20 cm. If the distance of the object is 30 cm from the lens, which of the following statements are correct for the position and height of the image?

• A. Position of the image is 15 cm
• B. Position of the image is 60 cm
• C. Height of the image is 8 cm
• D. Height of the image is -8 cm

Answer 1

Answer: (B), (D)

The correct options are
B Position of the image is 60 cm
D Height of the image is -8 cm

Let $u$ = image distance, Let $v$ = object distance, Let $f$ = focal length, Let $m$ = magnification.
Given:$f$ = 20 cm, $u$ = -30 cm, height of object = 4 cm (according to sign conventions)
Using lens formula: $\frac{1}{f}$ = $\frac{1}{v}$ - $\frac{1}{u}$
Putting values:
$\frac{1}{20}$ = $\frac{1}{v}$ - $\frac{1}{-30}$
or $\frac{1}{v}$ = $\frac{1}{20}$ - $\frac{1}{30}$
$\frac{1}{v}=\frac{3-2}{60}$
$v$ = 60 cm.
Distance of image from the lens is 60 cm.
magnification $m$ = $\frac{heightofimage}{heightofobject}$=$\frac{h^{\prime }}{h}$=$\frac{v}{u}$
$\frac{h^{\prime }}{4}$ = $\frac{60}{-30}$
or $h^{\prime }=-8cm$
Height of the object is -8 cm, which means the image is real and inverted.