When two plane mirrors are parallel, such as on opposite walls in a barber shop,
ID: 1504589 • Letter: W
Question
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 35 cm. The object is 5 cm in front of the left mirror and 30 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)
(c) Explain why each more distant image becomes fainter and fainter. (Do this on paper. Your instructor may ask you to turn in your work.)
Explanation / Answer
The first image in the mirror on the left is 5 cm behind the left mirror. The mirror on the right forms an image 30 cm behind that mirror or 65 cm from the left mirror. This image will result in a second image 65 cm behind the left mirror. The first image in the left mirror is 40 cm from the right mirror and forms an image 40 cm behind the right mirror or 75 cm from the left mirror. The second image in the left mirror is 65 cm from the right mirror and forms an image 100 cm behind the right mirror or 135 cm from the left mirror.
That image gives an image 75 cm behind the left mirror. This forms an image 110 cm behind the right mirror and 145 cm from behind the left mirror.
(a)
For the mirror on the left, the images are,
image 1 = 5 cm
image 2 = 65 cm
image 3 = 75 cm
image 4 = 135 cm
(b)
For the mirror on the right, the images are,
image 1 = 30 cm
image 2 = 40 cm
image 3 = 100 cm
image 4 = 110 cm
(c)
The successive images are dimmer because the light travels farther to form them. The intensity falls of inversely with the square of the distance the light travels. In addition, at each reflection a small percentage of the light intensity is lost. Real mirrors are not 100% reflecting.
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