Question

2. Grating of rectangular slits Take the solution from the workshop for a grating with M slits width Ax, Ay and spacing h given just for the x-axis by (TAx ) sin²(M Thu) I(x) = Ipeak sinca ( dz ) Msin(Thu) - 1 and design a grating where the 2nd order diffraction (second maxima of the term sin(M.)/ sin(.)) falls onto the first minimum of the single slit diffraction pattern. (a) find the condition for the 'strong' maxima of the quickly oscillating term (b) find the condition for h and Ar such that the second diffraction order vanishes. (c) A common grating used in the visible light (600nm) consists of 1200 lines/mm (assume that to mean number of rectangular apertures). What will be the angle tan 0 = x/z of the first and second order diffraction if you illuminate by a plane wave? (d) how much does the angle 8 change if you take a red (650nm) and green (532nm) laser pointer.

Answer 1

Answeclo A, for quickdy oscillating team, the strong marima are bound when =+M. lim Binti senimB) sinß wherre p = ahaldz and nzo, 21, 22.... this implies the required condition is B=0,11,12--... bi foor second oordeor of grating the condition is Chtm ) seh02 24 foor a single slits the biorst orden minimum is when Ansino at combrouing there two equations at the angle and wavelength is same we get vanishing of rewnd order when h= 4x Chena) seno at 633710 m where ht ALE 1

c'.Oz sent_600x109 8.33%107 0 = 46.08 e dar biorst oordeor lano = 1.03 Cht au) seho-zat heute in mm htax = 1200 htAx = 8.334157m 2x600x109 bor secondordeoi senos eX60 8.33X107 seho z1.44 Hence the second ordeur will no be visible dy for grating element of 8.33 xjö ?m Ming above equation of part c bour marne'ma 'the angle found tool

Oasent 650 x 10 9 .8338107 0-51.290 and tour 532 nm the angle bound is first ordeep 06 650mm w 02 cin' 532x109 8.33x10 0=39.70° Hence the change in the angle is 11.590