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

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

$n^{2} I_{0}, (n - 1) I_{0}$

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

$n I_{0}, I_{0}$

answer is A.

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Detailed Solution

$I n a c a s e o f i n t e r f e r e n c e o f t w o w a v e I = I_{1} + I_{2} + 2 \sqrt{I_{1} I_{2}} \cos ϕ (i) I n c a s e o f c o h e r e n t i n t e r f e r e n c e, ϕ d o e s n o t v a r y w i t h t i m e a n d s o I w i l l b e m a x i m u m w h e n \cos ϕ i s m a x i . e ., \cos ϕ = 1 {(I_{\max})}_{c o} = I_{1} + I_{2} + 2 \sqrt{I_{1} I_{2}} = {(\sqrt{I_{1}} + \sqrt{I_{2}})}^{2} s o f o r n i d e n t i c a l w a v e s e a c h o f i n t e n s i t y I_{0} {(I_{\max})}_{c o} = {(\sqrt{I_{0}} + \sqrt{I_{0}} + .....)}^{2} = {(n \sqrt{I_{0}})}^{2} = n^{2} I_{0} (i i) I n c a s e o f i n c o h e r e n t i n t e r f e r e n c e a t a g i v e n p o i n t, ϕ v a r i e s r a n d o m l y w i t h t i m e, s o {(\cos ϕ)}_{a v g} = 0 a n d h e n c e {(I_{a v g})}_{I n c o} = I_{1} + I_{2} S o i n c a s e o f n i d e n t i c a l w a v e s {(I_{a v g})}_{I n c o} = I_{0} + I_{0} + .............. = n I_{0}$