Principle: When final path of a ray of light after any number of reflections and refractions is reversed, the ray retraces back its entire path.
In Fig. ray of light travelling along AO in medium a is refracted along OB in medium b, at the interface XY.
Let ∠AON = i and ∠BON' = r
For incident ray
From Snell's law of refraction,
\(\frac{sin\ i}{sin\ r}\) = aµb ............(1)
Let a plane mirror M be held ⊥ to OB. The ray retraces its path and emerges along OA.
For the reversed beam
Angle of incidence i = angle of refraction r.
According to Snell's law,
\(\frac{sin\ r}{sin\ i}\) = bµa ..........(2)
Multiplying (1) and (2),
\(\frac{sin\ i}{sin\ r} \times \frac{sin\ r}{sin\ i}\) = aµb x bµa
i.e. 1 = aµb x bµa
or aµb = \(\frac{1}{b\mu_a}\)