It is possible to calculate the intensity in the single-slit Fraunbofer diffraction pattern without using the phasor method of Section 36.3. Let y’ represent the position of a point within the slit of width a in Fig. 36.5a, with y’ = 0 at the center of the slit so that the slit extends from y’ = â a/2 to y’ = a/2. We imagine dividing the slit up into infinitesimal strips of width dy’, each of which acts as a source of secondary wavelets.
(a) The amplitude of the total wave at the point O on the distant screen in Fig. 36.5a is E0. Explain why the amplitude of the wavelet from each infinitesimal strip within the slit is E0 (dy’/a ), so that the electric field of the wavelet a distance x from the infinitesimal strip is dE = E0(dy’/a) sin(kx â wt).
(d) Use the result of part (c) to show that if the intensity at point 0 is 10, then the intensity at a point P is given by Eq.(36.7).
(a) The amplitude of the total wave at the point O on the distant screen in Fig. 36.5a is E0. Explain why the amplitude of the wavelet from each infinitesimal strip within the slit is E0 (dy’/a ), so that the electric field of the wavelet a distance x from the infinitesimal strip is dE = E0(dy’/a) sin(kx â wt).
(d) Use the result of part (c) to show that if the intensity at point 0 is 10, then the intensity at a point P is given by Eq.(36.7).
