Question

In , a light wave along ray $r_1$ reflects once from a mirror and a light wave along ray $r_2$ reflects twice from that same mirror and once from a tiny mirror at distance $L$ from the bigger mirror. (Neglect the slight tilt of the rays) The waves have wavelength $\lambda$ and are initially exactly out of phase. What are the
(a) smallest,
(b) second smallest, and
(c) third smallest values of $L/\lambda$ such that result in the final waves being exactly in phase?

Answer 1

The equation can be given as ,

For $r_2{d}_1=4L$

$r_1{d}_2=2L$

When they are out of phase then the equation is ,

Path difference = $(n+0.5)\lambda$

4L-2L=$(n+0.5)\lambda$

L=$\frac{1}{2}(n+0.5)\lambda$

(a) when n=0

L=$\frac{1}{4}\lambda$

(b)when n=1

L=$\frac{3}{4}\lambda$

(c) when n=2

L=$\frac{5}{4}\lambda$