Question

Determine the angular spread between central maximum and first order maximum of the diffraction pattern due to a single slit of width `0.25 mm`, when light of wavelength `5890 Å` is incident on it normally ?

Answer 1

Half the angular spread `theta` between central maximum and first order maximum is given by
`a sin theta = (2n + 1)(lambda)/(2) = (2 xx 1+1)(lambda)/(2) = (3lambda)/(2)`
when `theta` is small, `sin theta ~~ theta :. Atheta = (3 lambda)/(2) or theta = (3 lambda)/(2 a) = (3 xx 5890 xx 10^(-10))/(2 xx 0.25 xx 10^(-3)) = 3.534 xx 10^(-3) rad`.
`:.` total angular spread `= +- 3.534 xx 10^(-3) rad`