Question

A 1.2-cm-wide diffraction grating has 1000 slits. It is illuminated by light of wavelength 510 nm. What are the angles of the first two diffraction orders? Answer = ∘,∘

Answer 1

Width of the grating w = 1.2 cm = 1.2 x10 ^-2 m

Number of slits N = 1000

wavelength = 510 nm = 510 x10 ^-9 m

Grating element d = w / N

                           = 1.2 x10 ^-5 m

Condition for first order is d sin =

   sin = / d

            = (510 x10 ^-9 ) /(1.2 x10 ^-5 )

            = 0.0425

         = 2.435 ^o

Condition for second order is d sin = 2

   sin = 2/ d

            = 2(510 x10 ^-9 ) /(1.2 x10 ^-5 )

            = 2(0.0425) = 0.85

         = 4.876 ^o