Given two plane mirrors. These mirrors are kept at the following angles one by one. From the below in which case the number of images formed is the maximum?

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30 °

60 °

45 °

90 °

answer is A.

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Detailed Solution

Given two plane mirrors. These mirrors are kept at the following angles one by one. The number of images formed at

30 °

is the maximum.
Plane mirror:
A plane mirror is a mirror with a ‘planar reflective surface’. For a plane mirror, angle of incident is the same as the angle of reflection.
The number of images (n) formed in two plane mirrors inclined at an angle P to each other is given by the below formula

Number of images n = 360 / P – 1

30 ° : number of images n = \frac{360 °}{30 °} = 12 - 1 = 11

60 ° : number of images n = \frac{360 °}{60 °} = 6 - 1 = 5

45 ° : number of images n = \frac{360 °}{45 °} = 8 - 1 = 7

90 ° : number of images n = \frac{360 °}{90 °} = 4 - 1 = 3

The number of images formed increases as the angle between the two plane mirrors decreases. This is because the number of images formed is indirectly proportional to the angle between them. Thus, choosing from options, a 30° angle can form the highest number of images.

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