An optician, while testing the eyes of a patient, keeps a chart of letters 3m behind the patient and asks her to see the letters on the image of the chart formed in a mirror kept at distance 2m in front of her. How far is the chart seen by the patient?
a. 3m
b. 2m
c. 6m
d. 7m

Hint: As we know for a plane mirror the distance of the image behind the mirror and the distance of the real object in front of the mirror both are the same. However, one can easily solve this problem by locating the object with respect to the mirror. So while reading the question, one should look for the data to locate the object with respect to the mirror, in order to solve this type of question quickly.

Complete step by step answer:


If the patient stands at a distance of 2 meters from a plane mirror, then her image will be formed at a distance of 2m behind the mirror. Here, the chart is kept at a distance of 3m behind the patient and she has a plane mirror in front of her at a distance of 2m.
Hence, we can now say that the distance of the chart (i.e. the object) from the plane mirror$ = 3 + 2 = 5m$

As discussed earlier, the image will form at the same distance behind the mirror as that of the object in front of the mirror.
So, the distance of image from the mirror $= 5m$

Now as we know that the patient is at a distance of 2m from the mirror. Hence, the distance of the image from her $= 5 + 2 = 7m$

Hence, the correct answer is option (D).

Note: One must always remember that, in case of a plane mirror the distance of the object from mirror $(d_o)$ is equal to the distance of the image $(d_i)$. i.e. ${d_o} = {d_i}$
Hence, the image is formed at a distance equal to that of the actual distance of the object from the mirror.