Optics Ques 17
- A concave mirror for face viewing has 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
(2019 Main, 9 April I)
(a) $0.16$ $ m$
(b) $1.60$ $ m$
(c) $0.32$ $ m$
(d) $0.24$ $ m$
Show Answer
Answer:
Correct Answer: 17.(c)
Solution:
Formula:
- Given, focal length of concave mirror,
$ f=-0.4 m $
Magnification $=5$
We know that, magnification produced by a mirror,
$ \begin{aligned} & m=-\frac{\text { image distance }}{\text { object distance }} \\ \Rightarrow \quad & \frac{v}{u}=-5 \text { or } v=-5 u \end{aligned} $
Using mirror formula,
$ \frac{1}{v}+\frac{1}{u}=\frac{1}{f} $
Substituting the given values in the above equation, we get
$\Rightarrow \frac{1}{-5 u}+\frac{1}{u} =-\frac{1}{0.4} $
$\Rightarrow \frac{4}{5 u} =-\frac{1}{0.4} $
$\Rightarrow u =-\frac{1.6}{5}=-0.32 $ $m$
Alternate Solution
Magnification produced by a mirror can also be given as
$ m=\frac{f}{f-u} $
Substituting the given values, we get
or
$ \begin{aligned} 5 & =\frac{-0.4}{-0.4-u} \\ u & =-0.32 m \end{aligned} $
BETA
