Question

The maximum intensity in case of interference of n identical waves, each of intensity I₀, if the interference is (i) coherent and (ii) incoherent respectively are

• A. $n^{2}I_{0},nI_{0}$
• B. $nI_{0},n^{2}I_{0}$
• C. $nI_{0},I_{0}$
• D. $n^{2}I_{0},(n - 1)I_{0}$

Answer 1

Answer: (A)

$n^{2}I_{0},nI_{0}$

Answer 2

In case of interference of two wave $I = I_{1} + I_{2} + 2\sqrt{I_{1}I_{2}}\cos\varphi$

(i) In case of coherent interference φ does not vary with time and so I will be maximum when $\cos\varphi = \max = 1$

i.e. $({Ic{o_{1}}_{2}\sqrt{I_{1}I_{2}}\sqrt{I_{1}}{\sqrt{I_{2}}}^{2}}_{\max}$

So for n identical waves each of intensity

I₀ $({Ico\sqrt{I_{0}}{\sqrt{I_{0}}}^{2}{{{\sqrt{I_{0}}}^{2}}^{2}}_{0}}_{\max}$

(ii)In case of incoherent interference at a given point, φ varies randomly with time, so $(\cos\varphi)_{av} = 0$ and hence

$(I_{R})_{Inco} = I_{1} + I_{2}$

So in case of n identical waves $(I_{R})_{Inco} = I_{0} + I_{0} + ....... = nI_{0}$