Light with wavelength `lambda = 589.0nm` falls normally on a diffraction grating with period `d = 2.5mu m`, comprising `N = 10 000` lines. Find the angular width of the diffraction maximum of second order.

Explanation

For the second order principle maximum
`d sin theta_(2) = 2lambda = k lambda`
or `(Npi)/(lambda)d sin theta_(2) = 2Npi`
minima adjacent to this maximum occur at
`(Npi)/(lambda)d sin (theta_(2)+-Delta theta) = (2N +-1)pi`
or `d cos theta_(2) = (lambda)/(N)`
Finally angular width of the `2^(nd)` principle maximum is
`2Delta theta = (2lambda)/(Nd cos theta_(2)) = (2lambda)/(Ndsqrt(1-(k lambda//d)^(2))) = (tantheta_(2))/(N)`
On putting the values we get `11.019''` of are