Question

Superposition of N harmonic oscillator waves of equal amplitude equal angular frequency ω and constant incremental phase difference φ. And constant spacing d between them. The total length of the array of the oscillator is L. With L = N*d

The amplitude is: where A0 the amplitude of each wave. A = A0 sin(Nφ /2) / sin(φ /2)

The intensity : I = I0*(sin(Nφ /2) / sin(φ /2))^2

1. show the minimum is at Nd*sin(θ ) = m λ, m =?

2. The principal maximum is at d*sin(θ ) = m λ 3. Secondary maximum is at Nd* sin(θ ) = (m+1/2) λ, m=? 4. Let β = Nφ , show that as N-> infinite and φ → 0 The intensity → I = 4 Im * ( sin(β/2) / β )^2 Where Im = N^2 * I0

5. show that minimum is at a*sin(θ ) = m λ and maximum is at a*sin(θ ) = (m+1/2) λ (Intensity drops drastically) Where a is the width of a single slit

6. Show that if I: intensity inversely square decreases of r, distance from the source, then the amplitude inversely decreases of r.

Answer 1