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^(@)`.

Find the wavelength of monochromatic light falling normally on a diffr

1.	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^(@)`.
Answer» 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`

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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^(@)`.

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