Question

Rakesh wants to obtain an image of size equal
to 1/3 of his actual size. At what distance
from a concave mirror of focal length 150 cm
should he stand?
​

Answer 1

Solution :-

Image height = 1/3 of Object height

⇒ hi = 1/3 * ho

⇒ hi/ho = 1/3

⇒ Magnification = - 1/3

Since magnification in a concave mirror is negative

Also, Magnification = - v/u

⇒ - 1/3 = - v/u

⇒ - u = - 3v

⇒ 3v = u

⇒ v = u/3

Focal length of the conncave mirror f = - 150 cm

By using mirror formula

⇒ 1/f = 1/v + 1/u

$\implies \tt \dfrac{1}{-150} = \dfrac{1}{ \dfrac{u}{3} } + \dfrac{1}{u}$

$\implies \tt \dfrac{1}{-150} = \dfrac{3}{ u } + \dfrac{1}{u}$

$\implies \tt \dfrac{1}{-150} = \dfrac{3 + 1}{ u }$

$\implies \tt \dfrac{1}{-150} = \dfrac{4}{ u }$

$\implies \tt u = 4(-150) = - 600$

Therefore he should stand at a distance of 600 cm in front of a concave mirror.