Two wavelength of sodium light `590 nm` and `596 nm` are used, in turn, to study the diffraction taking placed at a single slit of aperture `2 xx 10^(-4)m`. The distance between the slit and screen is `1.5 m`. Calculate the separation between the positions of first maxima of diffraction pattern obtained in the two cases.

Answer

`9 mm`

Explanation

Here, `lambda = 590 nm` and `lambda' = 596 nm`
`a = 2 xx 10^(-4) m`
and `D = 1.5 m`
For secondary maxima, the condition is
`a sin theta_(n) = (2n + 1)(lambda)/(2)` ltbr. First maxima of diffraction pattern corresponds to `n = 1`.
`:.` Separation of first maxima of diffraction pattern of two wavelength `= (2 xx 1 + 1)(lambda')/(2) - (3 lambda)/(2)`
`= (3)/(2)(lambda' - lambda) = (3)/(2)(596 - 590) = 9 nm`