"Let two plane mirrors are inclined at an angle theta.

Total deviation produced from two inclined plane mirror after two successive reflection is given by delta=360-2theta

The number of images formed n=(360/theta)-1, if (360/theta) is even integer..

If (360/theta) is odd integer, the number of images formed n=(360/theta)-1 when the object is kept symmetrically, and n=(360/theta) when object is kept asymmetrically..

If (360/theta) is a fraction, the number of images formed is equal to its integral part..

How do we get these relations"

Question

03-08-2016
Mathematics

Answered

"Let two plane mirrors are inclined at an angle theta.

Total deviation produced from two inclined plane mirror after two successive reflection is given by delta=360-2theta

The number of images formed n=(360/theta)-1, if (360/theta) is even integer..

If (360/theta) is odd integer, the number of images formed n=(360/theta)-1 when the object is kept symmetrically, and n=(360/theta) when object is kept asymmetrically..

If (360/theta) is a fraction, the number of images formed is equal to its integral part..

How do we get these relations"

Verified Answer :

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that θ−x is actually 180+2θ−x with respect to x-axis

When it emerges out, it should be 180−2θ+x with respect to x.
Considering our original x, the deviation is 180−2θ ... since it is in opposite direction, we should add 180 to it which makes 360−2θ

we take succesive images of every image on its opposite mirror till the image finally ends to the other side of the opposite mirror...

u should end up getting a arithmetic series for the angle for the image formed first 1 and i.this angle should not exceed 180 degree as the image will go behind the mirror..then the total no will be added for both to get the formula.