Question

Two identical coherent sources are placed on a diameter of a circle of radius $R$ at separation $x(<<R)$ symmetrically about the centre of the circle. The sources emit identical wavelength $\lambda$ each. The number of points on the circle with maximum intensity is $(x=5\lambda )$.

Answer 1

As the position of the bright fringe is given by,

$x_n=n\times \frac{D\lambda }{d}$

Here D=R, d=x=5$\lambda$, so the formula is modified as

$x_n=n\times \frac{R\lambda }{5\lambda }or,x_n=n\times \frac{R}{5}$, where n=0,1,2,3... for bright fringes.

When we put n=0, n=1, n=2, n=3, n=4 and n=5, we get the following bright positions,

$x_0=0,x_1=\frac{R}{5},x_2=\frac{2R}{5},x_3=\frac{3R}{5},x_4=\frac{4R}{5}$ and $x_5=R$

Therefore, total number of bright points on the circle=$(2\times 5)+1=11$