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 25 cm. The object is 15 cm in front of the left mirror and 10 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.)

Solutions

Expert Solution

Distance between mirrors D = 25 cm

Object distance from left mirror = 15 cm

Object distance from right mirror = 10 cm

For plane mirror,

Object distance = -Image distance

Image formed by plane mirror is virtual , so we take minus sign, but here we will ignore sign and just see magnitude

First image distance from Left mirror I_L1 = 15 cm

First image distance from Right mirror I_R1 = 10 cm

Fisrt image from right mirror acts as object for Left mirror

Second image on Left mirror I_L2 = Mirror distance + I_R1 = 25cm + 10cm = 35cm

Second image on Right mirror I_R2 = 25cm + I_L1 = 25cm + 15cm = 40cm

Third Image on Left mirror I_L3 = 25cm + I_R2 = 25cm + 40cm = 65cm

Third Image on Right mirror I_R3 = 25cm + I_L2 = 25cm + 35cm = 60 cm

Fourth Image on Left mirror I_L4 = 25cm + I_R3 = 25cm + 60cm = 85cm

Fourth Image on Right mirror I_R4 = 25cm + I_L3 = 25cm + 65cm = 90 cm

(a) Distance from left mirror to first four images

I_L1 = 15cm . I_L2 = 35cm, I_L3 = 65cm, I_L4 = 85cm

(b) Distance from right mirror to first four images

I_R1 = 10cm, I_R2 = 40cm, I_R3 = 60cm . I_R4 = 90cm

Thus the distant image becomes fainter and fainter.

genius_generous answered 1 year ago

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