Question

an object is kept at a distance of 20 cm from a convex mirror of focal length 15 cm find the position and magnification of the image

Answer 1

Given:

• Object mirror distance = u = 20 cm
• Focal length = f = 15 cm

To find:

Position (v) and magnification (m) of image = ?

Solution:

Applying Mirror formula:

$\sf{\dfrac{1}{f}=\dfrac{1}{v}+\dfrac{1}{u}}$

$\Rightarrow \: \sf{\dfrac{1}{15}=\dfrac{1}{v}+\dfrac{1}{20}}$

$\Rightarrow \: \sf{\dfrac{1}{v} = \dfrac{1}{15}-\dfrac{1}{20}}$

$\Rightarrow \: \sf{\dfrac{1}{v}=\dfrac{4-3}{60}}$

$\therefore \: \boxed{\bf{v = 60 \: cm}}$

Image position = 60 cm

For finding magnification,

$\sf{m=\dfrac{-v}{u}}$

$\to \sf{Magnification = \dfrac{-60}{20}}$

$\therefore \: \boxed{\bf{Magnification = -3}}$

KNOW MORE:

• The image is inverted and enlarged.