With light falling normally on a diffraction grating, the angle of diffraction of second order is equal to `45^(@)` for a wavelength `lambda_(1) = 0.65mum`. Find the angle of diffraction of third order for a wave length `lambda_(2) = 0.50 mu m`.

Explanation

From the fromula `d sin theta = m lambda`
we have `d sin 45^(@) =2lambda_(1) = 2 xx 0.65 mu m`
or `d = 2sqrt(2) xx 0.65mu m`
Then for `lambda_(2) = 0.50` in the thrid order
`2sqrt(2) xx 0.65 sin theta = 3 xx 0.50`
`sin theta = (1.5)/(1.3 xx sqrt(2)) = 0.81602`
This gives `theta = 54.68^(@) ~~55^(@)`