Question

An object is placed at a distance of $20cm$ from the pole of a concave mirror of focal length $10cm$. The distance of the image formed is?
A. $ + 20cm$
B. $ + 10cm$
C. $ - 20cm$
D. $ - 10cm$

Answer 1

Hint: We can solve this problem with the help of the concept of image formation by the concave mirror. Concave mirror has concavity towards forward and its concave surface acts like a reflecting surface. This mirror is also known as a converging mirror because it converges the light rays towards one focal point. If a parallel light rays falls upon its reflecting surface, this mirror converges them towards the focus.

Complete answer:
These mirrors are used to gather light and direct it in a beam so they are used in torches, spotlights and handlamps. The image formed by this mirror depends upon the initial positions of the object, if the object position varies then the image of the same object can be different. Hence the image formed by this mirror may be virtual, real, inverted, erect, small or large according to the object positions. For example, if the object presents between the focal point and the mirror the image is virtual, upright and magnified.

Focal length formula for the concave mirror is $\dfrac{1}{F} = \dfrac{1}{v} + \dfrac{1}{u}$, we use sign convention here.

For the given question, the object is placed in front of the mirror , distance of object is taken as negative and the focal length of the concave mirror is also negative , so
 $ \Rightarrow \dfrac{1}{v} + \dfrac{1}{{\left( { - 20} \right)}} = \dfrac{{ - 1}}{{10}}$
$ \Rightarrow \dfrac{1}{v} = - \dfrac{1}{{10}} + \dfrac{1}{{20}} = \dfrac{{ - 2 + 1}}{{20}} = - \dfrac{1}{{20}}$
$v = - 20cm$, hence the image of the object is $ - 20cm$ from the focal pole of the concave mirror.

So, the correct answer is “Option C”.

Note:
We know that a concave mirror is also called a converging mirror, it is also used in the telescope. While the convex mirror is also called a diverging mirror hence it is used in the rear view mirror in the vehicles.