Question

Fig. $29.17$(a) shows two coherent sources $S_1$ and $S_2$ which emit light of wavelength $\lambda$ in phase. The phase separation between the sources is $3\lambda$. A circular wire of radius $R>>I$ is placed symmetrically to $S_1$ and $S_2$ as illustrated. Find the angular positions $\theta$ on the wire for which constructive interference occurs.

Answer 1

The path difference $S_{1}K=S_1{S}_2\cos \theta =3\lambda \cos \theta$
For the constructive interference $3\lambda \cos \theta =n\lambda$
Putting $n=0,1,2$ and $3$.
$\theta ={90}^0$, $\theta ={\cos }^{-1}\frac{1}{3}$, ${\cos }^{-1}\frac{2}{3}$, $0^0$
We have listed positions of one quadrant. In other quadrants these positions will repeat.