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A person walks into a room that has, on opposite walls, two plane mirrors producing multiple images. Find the distances from the person to the first three images seen in the left-hand mirror when the person is 5.00 ft from the mirror on the left wall and 10.0 ft from the mirror on the right wall.

Sagot :

The distances of the person from the first three images as seen from the left hand mirror are 10.0 ft, 30.0 ft and 40.0 ft respectively.

From the question

The person is 5.00  ft from the mirror on the left wall

But the focal length of plane mirror is infinity which means both the image and object are equidistant from mirror

Therefore, the distance of first image on left wall of the mirror is

D1 = 5.00 + 5.00

     = 10.0 ft

where D1 is first distance.

So the image is 10.0 ft away from object.

From the second image,

The right side of the mirror forms the image of object at distance of 10.0 ft from the mirror on the right wall.

The person second distance is

d2 = (2 * 10.0) +10.0

d2 = 30.0 ft

where d2 is second distance.

And the third image is acquired by the addition of the image presented by the left mirror and the image presented by the right mirror.

d3 = (2 × 5.00) + 30.0

d3 = 40.0 ft

Therefore, the distances of the person from the first three images are 10.0 ft, 30.0 ft and 40.0 ft respectively.

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