Two identical coherent sources are placed on a diameter of a circle of radius R at a separation `d(ltltR)(d=nlambda)` symmetrically about the centre of the circle. The sources emit identical wavelength `lambda` each. What will be the number of points on the circle with constructive interference?

Options

A. `2n+1`
B. 4n
C. `4n-2`
D. `4n+2`

Answer

B

Explanation

For maxima `sintheta=(nlambda)/(d)`
`impliestheta=sin^(-1)((nlambda)/(d))`
So, no. of maxima in first quadrant is `(d)/(lambda)`. In second quadrant is `(d)/(lambda)`
So, in total no. of maximum `=(4d)/(lambda)` but out of these two are counted together so, actual no `=(4d)/(lambda)-2`