Optics 1 Question 2
2. 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) $0.24 m$
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Answer:
Correct Answer: 2. (c)
Solution:
- 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
$$ \begin{array}{rlrl} \Rightarrow & \frac{1}{-5 u}+\frac{1}{u} & =-\frac{1}{0.4} \\ \Rightarrow & \frac{4}{5 u} & =-\frac{1}{0.4} \\ \Rightarrow & & u & =-\frac{1.6}{5}=-0.32 m \end{array} $$
Alternate Solution
Magnification produced by a mirror can also be given as
$$ m=\frac{f}{f-u} $$
Substituting the given values, we get
or
$$ \begin{aligned} 5 & =\frac{-0.4}{-0.4-u} \\ u & =-0.32 m \end{aligned} $$
