Chapter 28, Problem 89GP

Predict/Calculate A system like that shown in Figure 28-35 consists of N slits, each transmitting light of intensity l₀. The light from each slit has the same phase and the same wavelength. The net intensity l observed at an angle θ due to all N slits is

$I=I_0{\left[\frac{\sin \left(N\varphi /2\right)}{\sin \left(\varphi /2\right)}\right]}^2$

In this expression, ϕ = (2πd/sinθ, where λ is the wavelength of the light (a) Show that the intensity in the limit θ→0 is l = N₂l₀. This is the maximum intensity of the interference pattern (b) Show that the first points of zero intensity on erther side of θ = 0 occur at ϕ = 2π/N and ϕ = −2π/N.