Find the wavelength of monochromatic light falling normally on a diffraction grating with period `d = 2.2 mu m` if the angle between the directions to the Fraunhofer maxima of the first and the second order is equal to `Delta theta = 15^(@)`.

Explanation

Given that
`d sin theta_(0) = lambda`
`d sin theta_(2) = d sin (theta_(1) + Delta theta) = 2lambda`
Thus `sin theta_(1)cos Delta theta + cos theta_(1) sin Delta theta = 2 sin theta_(1)`
or `sin theta_(1) (2- cos Delta theta) = cos theta_(1) sin Delta theta`
or `tan theta_(1) = (sin Delta theta)/(2- cos Delta theta)`
or `sin theta_(1) = (sin Delta theta)/(sqrt(sin^(2)Delta theta + (2-cosDelta theta)^(2)))`
`= (sin Delta theta)/(sqrt(5-4 cos Delta theta))`
Finally `lambda = (d sin Delta theta)/(sqrt((5 -4 cos Delta theta))`.
Substituation gives `lambda = 0.534 mu m`