Consider two perpendicular mirrors `M_(1)` and `M_(2)` and a point object O. Taking origin at the point of intersection of the mirrors and the coordinates of object as (x,y), find the position and number of images.

Explanation

As shown in Fig. , rays a and bb strike mirro `M_(1)` only and these rays will form image `I_(1)` at (x,-y), such that O and `I_(1)` are equidistant from mirror `M_(1)`. These rays do not form further image because they do not strike any mirror again. Similarly, rays 'd' and 'e' strike mirror `M_(2)` only and these rays will form image `I_(2)` at (-x,y), such that O and `I_(2)` are quidistant from mirror `M_(2)`.
Now, consider those rays which strike mirror `M_(2)` first and then the mirror `M_(1)`.
For incident rays 1,2 object is O, and reflected rays 3,4 form image `I_(2)`.
Now, rays 3, 4 incident on `M_(1)`(object is `I_(2)`) reflect as rays 5,6 and form image `I_(21)`. Rays 5, 6 do not strike any mirror, so image formation stops.
`I_(2)` and `I_(21)` are equidistant from `M_(1)`. to summarize, see Fig.
For rays reflecting first from `M_(1)` and then from `M_(2)`, first image `I_(1)` ( at(x,-y)) will be formed. `I_(1)` will act object for mirror `M_(2)` and then its image `I_(12)` (at (-x, -y))` will be formed. `I_(12)` and `I_(21)` coincide.
Hence, three images are formed.
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