An inteference is observed due to two coherent sources A and B separated by a distance `4lambda` along Y-axis, where `lambda` is the wavelength of light. A detector 'D' is moved alog the positive X-axis. Find the totla number of maxima observe on the X-axis excluding the points `x =0` and `x = oo` ?

Answer

3

Explanation

To obtain maxima the path difference
`AD-BD = n lambda`
`AD-x_(n) = n lambda`
`AD = n lambda + x_(n) rarr (1)` From `Delta_(le) ABD`,
`AD^(2) = AB^(2) + BD^(2) (n lambda + x_(n))^(2) = 16lambda^(2) + x_(n)^(2)`
`n^(2)lambda^(2)+x_(n)^(2)+2n lambda x_(n) = 16 lambda^(2) + x_(n)^(2)`
`2n lambda x_(n) = (16 - n^(2))lambda^(2) x_(n) = ((16-n^(2))lambda)/(2n)`
For `n = 0 implies x_(0) = oo`
`n = 1 implies x_(1) = ((16-1)/(2))lambda = (15lambda)/(2) = 7.5lambda`
`n = 2 implies x_(2) = ((16-4)/(4))lambda = (12lambda)/(4) = 3 lambda`
`n = 3 implies x_(3) = ((16-9)/(6))lambda = (7lambda)/(6)`
`n = 4 implies x_(4) = ((16 - 16)/(2xx4))lambda = 0`
So the total no.of maxima points observed are 3.