Question

Two coherent sources A and B with separation 2λ are placed the x axis symmetrically about the origin.they emit light of wave lengthλ.obtain the positions of maximas on a circle of large radius R lying in the xy plane and with the centre at origin

Answer 1

Condition for maxima is given by path difference and phase difference.

Here path difference is calculated by drawing perpendicualr on AB,

So, path difference from fig will be,

$\Delta x=2\lambda cos\theta =n\lambda$

$cos\theta =\frac{n}{2}$

For maxima path difference should be $=n\lambda$ where, $=0,1,2,\mathrm{3.............}$

$n=\pm 1and\pm 2$

$\theta =60,120^o,{90}^o,{270}^o,{240}^o,{300}^o$

Since sources are symmetrical we use both positive and negative values.

And we will get 8 maxima point as shown below: