Question

A concave mirror for face viewing has 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:
A. 1.60m
B. 0.24m
C. 0.16m
D. 0.32m

Answer 1

Hint: Focal length of concave mirror is the distance between the pole of mirror and the focus. To get an image which is upright and larger than the object, the object must be placed between the focus and the pole behind the mirror.

Complete step by step answer:

Given,
Focal length of concave mirror, f=0.4m
Magnificent of image to object, m=5
Magnification, $m=\dfrac{v}{u}$
Here, v is the distance of image from the pole of mirror
u is the distance of image from the pole of mirror
$5=\dfrac{v}{u}$
$v=5u$
By using mirror formula-
\[\dfrac{1}{v}+\dfrac{1}{u}=\dfrac{1}{f}\]
Here, we substitute the v in terms of u that we calculated above-
$\dfrac{1}{5u}+\dfrac{1}{(-u)}=\dfrac{1}{(-0.4)}$
$\dfrac{1}{u}(\dfrac{1}{5}-1)=-\dfrac{1}{0.4}$
$u=\dfrac{-4}{5}\times 0.4$
$u=-0.32m$
Here, ‘-ve’ sign shows that the object is in front of the mirror.
The mirror is kept at a distance of 0.32m from the face.

Additional Information:
The concave mirrors provide the wide range of its usage in the field of medical, astronomical, automobile and for household also. Its characteristic of producing magnified images make these concave mirrors to be used in telescopes, headlight etc. Also, these are capable of producing many types of combinations of images such as erect and inverted, real and virtual and small and magnified.

Note: As mirrors have their own sign conventions with respect to the position of object and image. So, proper use of sign conventions must be followed in order to get the correct answer. A proper approach to these types of questions must be through drawing a neat and logical diagram.