Question

# When two plane mirrors are parallel, such as on opposite walls in a barber shop, multiple...

When two plane mirrors are parallel, such as on opposite walls in a barber shop, multiple images arise because each image in one mirror serves as an object for the other mirror. An object is placed between parallel mirrors separated by 40 cm. The object is 5 cm in front of the left mirror and 35 cm in front of the right mirror.

(a) Find the distance from the left mirror to the first four images in that mirror.
cm (image 1)
cm (image 2)
cm (image 3)
cm (image 4)

(b) Find the distance from the right mirror to the first four images in that mirror.
cm (image 1)
cm (image 2)
cm (image 3)
cm (image 4)

Let us denote left mirror as m1 and right mirror as m2.

The question can be solved by using the concept of multiple reflections in case of parallel mirrors in which image formed by one mirror acts as an object for other after the first image has been formed. The distances of first four images formed by m1 are 5, 75, 155 and 235 m respectively. And those by m2 are 35, 115, 195, 275 m respectively.

The first image is of the object placed infront of the mirror. For formation of second image, the 1st image on opposite side acts a object, hence the distance of second image is sum of distance between the 2 mirrors and the distance of 1st image from opposite mirror.

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