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 `M_(1)` only and these rays will from image `I_(1)` at `(x, -y)` such that `O` and `I_(10` are equidisant form mirror `M_(1)`. These rays do not form further image because they do not strike any mirror again. Similarly rays `'d'` and `'e'` strike any mirror `M_(2)` only and these rays will form image `I_(2)` at `(-x,y)` such that `O` and `I_(2)` are equidistant form mirror `M_(2)`.

Now consider those rays whic strike mirror `M_(2)` first and then the mirror `M_(1)`

For incident rays `1,2` object is `O`, and reflect 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_(2)`. Rays `5,6` do not strike any mirror, so image formation stops.
`I_(2)` and `I_(21)`, are equildisatant form `M_(1)`. To summarize see the following figure.

For rays reflecting first form `M_(1)` and then form `M_(2)` first image `I_(1)` (at `(x,-y)` ) will be formed adn this will funcion 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.