Question

An object is placed at a distance 20cm from the pole of a convex mirror of focal length 20cm. The image is produced.
A. 13.3cm
B. 20cm
C. 25cm
D. 10cm

Answer 1

Hint: You could first note down the given values in the question keeping the sign conventions in mind. Then you could make the corresponding ray diagram just to get a clear picture of the given situation. Now you could simply substitute the given values to get the magnitude of image distance.

Formula used:
Mirror Formula,
$\dfrac{1}{f}=\dfrac{1}{v}+\dfrac{1}{u}$

Complete answer:
In the question, we are given a convex mirror of focal length (f) 20cm and the object distance (u) as 20cm from the pole. Using this information, we are supposed to find the image distance. Let us make a ray diagram of the given situation.

We have made the image in the diagram using two rules. They are,
(1) Ray parallel to the principal axis will converge to the focal point or appear to diverge from the focal point.
(2) The Ray incident at the pole of a mirror will reflect making equal angles at the pole.
Now, in order to find the image distance, we could make use of the mirror formula which is given by,
$\dfrac{1}{f}=\dfrac{1}{v}+\dfrac{1}{u}$
$\Rightarrow v=\dfrac{uf}{u-f}$
Substituting the given values we get,
$v=\dfrac{-20\times 20}{-20-20}$
$\Rightarrow v=\dfrac{-400}{-40}$
$\therefore v=10cm$
Therefore, we have found the image distance to be 10cm behind the mirror.

Hence, option (D) is the correct answer.

Note:
At the very first glance at the question, you may think that the object is kept at the focus of the mirror. This is where the type of mirror and hence the corresponding sign conventions has great significance. The nature of the image so formed is virtual, erect and diminished.