Two wavelength of sodium light of 590 nm and 596 nm are used in turn to study the diffraction taking place at a single slit of aperture `2xx 10^(-6)` m. The distance between the slit and the screen is 1.5 m. Calculate the separation between the positions of first maxima of the diffraction pattern obtained in the two cases.

Explanation

Angular position of first maxima, ` x = (lambdaD)/(a) ` where, D = 1.5m , a = `2xx10^(-6)`m
For `lambda = 590 nm`,
`x_(1) = (590xx 10^(-9) xx 1.5)/(2xx 10^(-6)) = 0.4425 m = 44.25 cm`
For `lambda` = 590 nm,
`x_(2) =(590xx 10^(-9) xx 1.5)/(2xx 10^(-6)) = 0.447 m = 44.7 cm`
`therefore` Separation `= x_(2) - x_(1) = 0.45 cm`