Question

Figure shows two inclined plane mirros `M_(1)` and `M_(2)` and an object `O`. Its image formed in mirrors `M_(1)` and `M_(2)` individually and `I_(1)` and `I_(2)` respectively. Show that `I_(1)` and `I_(2)` and `O` lie on the circumference of a circle with centre at `I`. [This result can be extended to show that all the images will also lie on teh same circle. Note that this result is independent of the angle of inclination of mirrros.]. `I` is the point of intersection fo the mirrors.

Answer 1

Clearly
`Delta IOQ` and `Delta I_(2) Q` are congruent
and `Dleta IOP` and `Delta II_(1)P` are congurent
So `II_(1) = IO` and `IO = II_(2)`
Hence, `II_(1) = IO = II_(2)`
So, `I_(1)` and `I_(2)` and `O` lie on the circumference of a circle with centre `I`.