This is very easy, if the given is one mirror (iR=rR) or the incident ray is equal to reflected ray. If the given is two or more, to find the reflected ray you need to know the measure of the angle formed by the two mirrors, the mathematical solution for this is the |Reflected ray of mirror 1 + Reflected ray of mirror 2| = |the measurement of the angle that mirror 1 and 2 form| or when transmuted |m(angle)m1,m2-iRM1|=rRM2 .

For example, there are 3 mirrors. Second mirror is 100 degrees to the left of the First mirror, and the third mirror is 40 degrees to the left of the second mirror. The Incident ray hit mirror 1 at an angle of 40 degrees the reflected angle of mirror is 60 degrees following the given formula (|[m(angle)m1,m2]-iRM1|=rRM2) or (|100-40|=60) so it follows that the Reflected Ray of mirror 3 is 20 degrees using the formula again.

It's very simple and easy, this is the "so called" shortcut. ^_^