Question

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

• A. $3$m
• B. $2$m
• C. $6$m
• D. $7$m

Answer 1

The correct option is D $7$m

For plane mirrors, the object distance (do) is equal to the image distance (di). That is, the image is the same distance behind the mirror as the object is in front of the mirror. If we stand a distance of 2 meters from a plane mirror, we must focus at a location 2 meters behind the mirror in order to view our image.
In this case, a chart of letters is kept 3 m behind the patient and is asked to see the letters on the image of chart formed in a plane mirror kept at distance 2m in front of her. Therefore, the total distance from the chart and the mirror is 3 m+2 m=5 m.
As the object distance and image distance are equal, the image is formed at a distance of 5 m behind the mirror. The patient is at a distance of 2m from the mirror.
Hence, the total distance covered in viewing the image of the letters on the cart is 5 m+2 m = 7 m.