Find the maximum intensity in case of interference of n identical waves each of intensity Io if the interference is
(i) coherent (ii) incoherent

Solution

Given, n identical waves, each of intensity I_o.

(i) In case of two coherent sources, resultant intensity is given by,

I_{R} = I_{1} + I_{2} + 2 \sqrt{I_{1} I_{2}} \cos ϕ

I_{R}

will be maximum when,

\cos ϕ = 1 (maximum)

So for n identical waves each of intensity I₀,

∴

(I_{\max})_{\infty} = I_{1} + I_{2} + 2 \sqrt{I_{1} I_{2}}

(I_{\max})_{\infty} = {(\sqrt{I_{0}} + \sqrt{I_{0}} . . . . . .)}^{2}

= {(\sqrt{I_{1}} + \sqrt{I_{2}})}^{2}

= {(n \sqrt{I_{0}})}^{2} = n^{2} I_{0}

(ii) In case of incoherent sources, resultant intensity is given by,

I_R = I₁+ I₂ + ............
= I₀ + I₀+ .............
= nI₀.

For Daily Free Study Material Join wiredfaculty