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

Explanation

Rays 'a' and 'b' strike mirror M1 only and these rays will form image `I_(1)` at (x, –y), such that O and I1 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 equidistant from mirror `M_(2)`.
Now consider those rays which strike mirror `M_(2)` first and then the mirror `M_(1)`.
For incident ray 1,2 object is O, and reflected rays 3, 4 from image `I_(2)`.
Now rays 3, 4 incident on `M_(1)` (object is `I_(2)`) which 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 the following figure Now rays 3,4 incident on `M_(1)` (object is `I_(2)`) which reflect as rays 5, 6 and form image `I_(21)`. Rays 5, 6 do not strike any mirror, so image formation stops.
For rays reflecting first from `M_(1)` and from `M_(2)`, first image `I_(1)` at (x, –y) will be formed and this will function as object for mirror `M_(2)` and then its image `I_(12)` (at (–x, –y)) will be formed. `I_(12)` and `I_(21)` coincide.
`:.` Three images are formed