Question

• A monochromatic light of wavelength λ=600nm illuminates a grating with normal incidence. The diffraction angle corresponding to the second order principle maximum is 30°and the third order is missing. (1) What is the grating spacing (a+b)? (2) what is the possible least width of a ruling a? (3) If the spacing and the ruling are given as above, find all the possible orders of principle maximum in the range of -π/2<θ<π/2 ?

Answer 1

Part 1

$d sin \theta = n \lambda$

$(a+b) sin 30 = 2*600$

$a+b =2400*10^{-9} = 2.4 * 10^{-6} =2.4 \mu m$

Part 2

$\frac{asin \theta}{dsin \theta}=\frac{\lambda}{3\lambda} \implies a = \frac{d}{3}= \frac{2.4}{3}=0.8 \mu m$

Part 3

The possible orders of principle maxima

n=-2,-1,0,1,2

as the third order is missing order.