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Question

In the figure you are in a system of two vertical parallel mirrors A and B separated by distance d. A point object is placed at point O, a distance 0.2d from mirror A. Each mirror produces a first (least deep) image of the object. Then each mirror produces a second image with the object being the first image in the opposite mirror. Then each mirror produces a third image with the object being the second image in the opposite mirror, and so on - you might see hundreds of  images. How deep behind mirror A are the first, second, and third images in mirror A? 

  1. 0.2d, d and 2d
     
  2. 0.2d, 1.8d and 2.2d
     
  3. 0.2d, 1.6d and 2.2d
     
  4. can′t be calculated.
     


Solution

The correct option is B 0.2d, 1.8d and 2.2d
 
Lets understand it from the diagram shown below : 


Looking from the diagram the first image in mirror B is at a distance 1.8d from the Mirror A, hence it will be at a depth 1.8d inside the mirror A. 

Again looking at the diagram, The first image in Mirror A (Which is the object for the second image in Mirror B) is at a distance 1.2d from Mirror B, hence it is 1.2d distance deep in Mirror B. 

Now, that is the second image in Mirror B which is the third object for Mirror A and at a distance 2.2d from the Mirror A.

Hence the third image is 2.2d deep inside Mirror A. 

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