Prove the relation `""^(a)mu_(b)=1/(""^(b)mu_(a))`

Explanation

By the principle of reversibility we know that if a ray of light after suffering a number of reflections or refractions, finally falls normally on a plane mirror then its path is reversed.
Fig shows a ray of light AB refraction at the boundary XY separating the two media, falls normally on the plane mirror M and gets reflected back and retraces its path.
Using Snell.s law for incident ray:

`""^(a)mu_(b)=(sini)/(sinr)` ............1
For reflected ray: `""^(b)mu_(a)=(sinr)/(sini)`.........2
Multiplying 1 and 2 `""^(a)mu_(b)xx""^(b)mu_(a)=1`
`""^(b)mu_(a)+1/(""^(a)mu_(b))`