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Two plane mirrors are placed parallel to each other at a distance L apart. A point object O placed between them, at a distance L/3 from obe mirror. Both mirros form multiple image. The distance between any two images cannot be
- a)3L/2
- b)2L/3
- c)2L
- d)L
Correct answer is option 'A'. Can you explain this answer?
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Two plane mirrors are placed parallel to each other at a distance L ap...
Given:
Two plane mirrors are parallel to each other at a distance L.
A point object O is placed between them, at a distance L/3 from one mirror.
To find:
The distance between any two images formed by the mirrors.
Solution:
Let us first find the position of the first four images of the object O.
Image formation by a single mirror:
When an object is placed in front of a mirror, its image is formed behind the mirror.
The image is virtual, i.e., it cannot be obtained on a screen.
The distance of the image from the mirror is equal to the distance of the object from the mirror.
The image is laterally inverted, i.e., left appears as right and vice versa.
Image formation by two parallel mirrors:
When an object is placed between two parallel mirrors, its image is formed by multiple reflections.
Each image acts as a virtual object for the next reflection.
The number of images formed is infinite, but they become progressively dimmer and smaller.
Let us consider the given situation.
Position of the first image:
The first image of the object O is formed by a single reflection from one of the mirrors.
Let us assume that it is formed by reflection from the mirror on the left side.
The image is virtual and appears behind the mirror on the right side.
The distance of the image from the mirror on the left side is L/3, and the distance of the image from the mirror on the right side is 2L/3.
Therefore, the position of the first image is at a distance of 2L/3 + L/3 = L from the mirror on the right side.
Position of the second image:
The second image of the object is formed by two reflections.
The first reflection is from the mirror on the right side, which forms an image at a distance of L/3 from it.
The second reflection is from the mirror on the left side, which forms an image at a distance of L/3 from it.
Therefore, the position of the second image is at a distance of 2L/3 + L/3 + L/3 = L + L/3 = 4L/3 from the mirror on the right side.
Position of the third image:
The third image of the object is formed by three reflections.
The first reflection is from the mirror on the right side, which forms an image at a distance of 4L/3 from it.
The second reflection is from the mirror on the left side, which forms an image at a distance of 4L/3 from it.
The third reflection is from the mirror on the right side, which forms an image at a distance of L/3 from it.
Therefore, the position of the third image is at a distance of 2L/3 + 4L/3 + L/3 = 3L from the mirror on the right side.
Position of the fourth image:
The fourth image of the object is formed by four reflections.
The first reflection is from the mirror on the right side, which forms an image at a distance of 3L from it.
The second reflection is from the mirror on the left side, which forms an image at a distance of 3L from it.
The third reflection is from the mirror on the right side, which forms an image at a distance of 4L/3 from it.
The fourth reflection is from the mirror on the left side, which forms
Two plane mirrors are parallel to each other at a distance L.
A point object O is placed between them, at a distance L/3 from one mirror.
To find:
The distance between any two images formed by the mirrors.
Solution:
Let us first find the position of the first four images of the object O.
Image formation by a single mirror:
When an object is placed in front of a mirror, its image is formed behind the mirror.
The image is virtual, i.e., it cannot be obtained on a screen.
The distance of the image from the mirror is equal to the distance of the object from the mirror.
The image is laterally inverted, i.e., left appears as right and vice versa.
Image formation by two parallel mirrors:
When an object is placed between two parallel mirrors, its image is formed by multiple reflections.
Each image acts as a virtual object for the next reflection.
The number of images formed is infinite, but they become progressively dimmer and smaller.
Let us consider the given situation.
Position of the first image:
The first image of the object O is formed by a single reflection from one of the mirrors.
Let us assume that it is formed by reflection from the mirror on the left side.
The image is virtual and appears behind the mirror on the right side.
The distance of the image from the mirror on the left side is L/3, and the distance of the image from the mirror on the right side is 2L/3.
Therefore, the position of the first image is at a distance of 2L/3 + L/3 = L from the mirror on the right side.
Position of the second image:
The second image of the object is formed by two reflections.
The first reflection is from the mirror on the right side, which forms an image at a distance of L/3 from it.
The second reflection is from the mirror on the left side, which forms an image at a distance of L/3 from it.
Therefore, the position of the second image is at a distance of 2L/3 + L/3 + L/3 = L + L/3 = 4L/3 from the mirror on the right side.
Position of the third image:
The third image of the object is formed by three reflections.
The first reflection is from the mirror on the right side, which forms an image at a distance of 4L/3 from it.
The second reflection is from the mirror on the left side, which forms an image at a distance of 4L/3 from it.
The third reflection is from the mirror on the right side, which forms an image at a distance of L/3 from it.
Therefore, the position of the third image is at a distance of 2L/3 + 4L/3 + L/3 = 3L from the mirror on the right side.
Position of the fourth image:
The fourth image of the object is formed by four reflections.
The first reflection is from the mirror on the right side, which forms an image at a distance of 3L from it.
The second reflection is from the mirror on the left side, which forms an image at a distance of 3L from it.
The third reflection is from the mirror on the right side, which forms an image at a distance of 4L/3 from it.
The fourth reflection is from the mirror on the left side, which forms
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Two plane mirrors are placed parallel to each other at a distance L apart. A point object O placed between them, at a distance L/3 from obe mirror. Both mirros form multiple image. The distance between any two images cannot bea)3L/2b)2L/3c)2Ld)LCorrect answer is option 'A'. Can you explain this answer?
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