A concave mirror for face viewing has a focal length of 0.4 m . The distance at which you hold the mirror from your face in order to see your image upright with a magnification of 5 is

Question

A concave mirror for face viewing has a focal length of 0.4 m . The distance at which you hold the mirror from your face in order to see your image upright with a magnification of 5 is (A) 1.60 m (B) 0.16 m (C) 0.32 m (D) 0.24 m

Tardigrade Admin · Accepted Answer

m=5=-(v/u)⇒ v=-5u f=-0.4 m From mirror formula, (1/v)+(1/u)=(1/f) (1/- 5 u)+(1/u)=(1/- 0 .4) (- 1 + 5/5 u)=(1/- 0 .4) u=(4/5)(- 0 .4)=-0.32 m So, distance of object from mirror =0.32 m

Q. A concave mirror for face viewing has a focal length of $0.4 m$ . The distance at which you hold the mirror from your face in order to see your image upright with a magnification of $5$ is

$1.60 m$

$0.16 m$

$0.32 m$

$0.24 m$

$m = 5 = - \frac{v}{u} \Rightarrow v = - 5 u$
$f = - 0.4 m$
From mirror formula,
$\frac{1}{v} + \frac{1}{u} = \frac{1}{f}$
$\frac{1}{- 5 u} + \frac{1}{u} = \frac{1}{- 0.4}$
$\frac{- 1 + 5}{5 u} = \frac{1}{- 0.4}$
$u = \frac{4}{5} (- 0.4) = - 0.32 m$
So, distance of object from mirror $= 0.32 m$

Q. A concave mirror for face viewing has a focal length of 0.4m . The distance at which you hold the mirror from your face in order to see your image upright with a magnification of 5 is

1.60m

0.16m

0.32m

0.24m