Answer Happy

Please for the sketches do not copy other experts, the
sketches should appear as similar to tophat functions similar to
this: Answer all parts.
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Equation 4.2 if needed
u We can extend the techniques of the previous section to calculate the diffraction pattern from a multiple slit grating of N slits of width a and spacing d. We define the 'grating' function to be N-1 8(x) = { 8(x-nd). (4.12) n=0 al Sketch the aperture function for an N-slit zero width grating (Eq. 4.12) as a function of x. By substituting 8 (x) from Eq. 4.12 for A (x) in Eq. 4.2 it can be shown that the intensity pattern for a zero width N-slit grating is given by sin? (NB) 1(0) sin? (B) where B = d sin (C). (4.13) 6 Sketch the aperture function of an N-slit grating of slit width a and slit spacing d as a function of x. Using arguments similar to those used earlier (Q5 and following text) explain why the intensity dis- tribution for diffraction from an N-slit grating is given by sin? (a) ? 1(0)=1(0) (4.14) a a) (sin? (NB) sin? (B) ) = (1/2)a sin (0) and where a (1/2)d sin (O). B

= Optics course, the amplitude of the far-field diffrac- tion pattern is the Fourier transform of the transmission function of the diffracting aperture: Ares (0) = LA(x)exp(-ikxsin (O))dr, (4.1) and the observed intensity 1 (0) = |Ares? is given by 1(0) = LA A (x) exp[-ikxsin (0)]dx (4.2) where Ares is the resultant amplitude at an angle e, with e being the angle between the straight through direc- tion and a point on the pattern. Here the aperture func- tion A (x) represents the wave amplitude at a position x along the source, and k = 21/2 for monochromatic light of wavelength 2.