Two coherent sources emit light of wavelength `lambda`. Separation between them, `d = 4 lambda`.

If a detector moves along the y-axis, what is the maximum number of minima observed?

Options

A. 6
B. 9
C. 5
D. 4

Answer

b

Explanation

The path difference at any point on the screen is
`d sin theta = n lambda`
`implies n = (d)/(lambda) sin theta`
n is maximum when `theta` ia maximum, thus maximum value of n is
`n = (d)/(lambda) = 4`
Hence, number of minima are four approximately correspondind to path difference
`Delta x = (lambda)/(2) , (3 lambda)/(2) , (5 lambda)/(2) , (7 lambda)/(2)`
Thus, apart from central maxima at `theta = 0`, eight other maxima, 4 on either side of central maxima are registered. Total maxima registered are 9 and 8 minima lie between them.
The path difference at any point Q on the x-axis is
`Delta X = AQ - BQ = (AB)/(cos theta) (1 - sin theta)`
Condition for maxima is
`(d)/(cos theta) (1 - sin theta) = n lambda`
`n = (4 (1 - sin theta))/(cos theta)`
At point B, `theta = 0 implies n =4`, i.e.,we get fourth-order maxima.
At `x = prop, theta = pi // 2`, path difference is zero
Thus, at `theta = pi // 2`, we have `n = 0`, i.e., zeroth-order maxima is formed at `x = infty`.
Hence, along x-axix, beginning from slit B fifth-order maxima are registered.