Question

Derive the deriavtion formula for single slit diffraction

Answer 1

Intensity of single slit diffraction

1. General considerations

Following Giancoli, section 35-2 (and quoting some of the text), we consider the single slit divided

up into N very thin strips of width ∆y as indicated in the figure below. Note that the width of the slit

is D = N∆y. This is an approximate description of an actual slit of width D. This approximation

becomes exact in the limit of N → ∞ and ∆y → 0, where these two limits are to be taken in such

a way that the product N∆y = D is fixed.

Each strip sends light in all directions to a screen on the right. We take the rays heading for

any particular point on the distant screen to be parallel, with all rays making an angle θ with the

horizontal as shown above. We choose the strip width ∆y ≪ λ so that all the light from a given

strip is in phase. The strips are of equal size, and if the whole slit is uniformly illuminated, we can

take the electric field wave amplitudes from each thin strip to be equal. The amplitude of the wave

emanating from each thin strip is given by

∆E0 =

E0

N

,

where E0 is the amplitude of the wave incident on the single slit. The outgoing waves from the

different strips will differ in phase at the screen. The phase difference in the light coming from