If two coherent source are placed at a distance `3lambda` from each other, symmetric to the centre of the circel as shown in figure, Find thenumber of fringes shown on the screen, placed along the circumference ?

Options

A. 16
B. 12
C. 8
D. 4

Answer

B

Explanation

Path difference at any point 'P' on the circumference

`Delta x = S_(1)P - S_(2)P S_(1) P = R + (3lambda)/(2)cos theta`
`S_(2)P = R - (3lambda)/(2)cos theta Delta x = S_(1)P - S_(2)P`
`Delta x = 3lambda cos theta` For maxima at 'P'
`Delta x = n lambda = 3lambda cos theta`
`cos theta = (n)/(3) [n = 0,1,2,3,---]`
`cos theta = 0, (1)/(3), (2)/(2), 1` [maximum value of `cos theta = 1`]
`:.` In each quadrant there are 3 maximas. Hence in 4 quadrants there willbe 12 maximas. Hence 12 minima in between so there are 12 fringes