Correct Answer - Option 3 : 0.32 m
Concept:
In a concave mirror, the magnification is the ratio of the height of the image to the height of the object. The magnification is also equal to the negative of the ratio of the distance of the image from the mirror to the distance of the object from the mirror.
It is represented as the ratio of the height of the image to the ratio of the height of the object. Magnification is denoted as the letter ‘m’. Where,
Magnification (m) = h/h’
Calculation:
Given,
Focal length, f = 0.4 m
Magnification, m = +5
u is the distance of the object from pole and v is the distance of the image from the pole.
Now +v means, image is towards up to the principal axis i.e. image is erect.
-v means the image is to downward of the principal axis. i.e. image is inverted.
Magnification can also be related to the image distance and object distance; therefore, it can also be written as:
\(m = + 5 = - \frac{v}{u} \Rightarrow v = - 5u\)
Using Mirror formula,
\(\frac{1}{v} + \frac{1}{u} = \frac{1}{f}\)
\(\Rightarrow \frac{1}{{ - 5u}} + \frac{1}{u} = \frac{{ - 1}}{{0.4}}\)
\(- \frac{1}{{0.4}} = - \frac{4}{{5u}}\)
\(u = \frac{4}{5} \times \frac{{0.4}}{1}\)
∴ u = 0.32 m
The distance at which you hold the mirror from your face in order to see your image upright is 0.32 m
