Question

n identical waves each of intensity Io interfere with each other.The ratio of maximum intensities if the interference is i) coherent ii) incoherent is:

Answer 1

what does coherent interference mean?

Answer 2

Generation from a same source

Answer 3

yeah but how will that affect the interference?

Answer 4

There we can get constant phase difference all the time...
In case of coherent sources

Answer 5

oh.. can you explain how to solve this Q.. coz i still didn't get a clear picture..

Answer 6

@agent0smith

Answer 7

@samigupta8 @ganeshie8

Answer 8

Is the answer \(n^2\) for coherent and \(n\) for incoherent ?

Answer 9

just the ratio is given which is correct... so your answer is correct1 now, pls tell me hoe to solve..

Answer 10

the ratio is n

Answer 11

@ganeshie8 ?

Answer 12

Consider the electric field of one light wave at a specific point, say, \(x = 0\) :
\[E_1 = E_0\sin(\omega t)\tag{1}\]

Answer 13

If the light waves are coherent (same frequency, phase), then the electric fields of remaining waves also follow the same equation as above.

Answer 14

Add up the electric fields and get
\[E_{net} = nE_0 \sin(\omega t)\]

Answer 15

Next, use the fact that \(I \propto E^2 \)

Answer 16

ok.. so max. intensity will be n^2 .. but for the second case we can't add them as they won't have const. phase diff right?

Answer 17

@ganeshie8

Answer 18

@mayankdevnani

Answer 19

@ganeshie8 how did you get n as max. intensity for incoherent?

Answer 20

i got `n` as answer ?

Answer 21

hope this is correct !

Answer 22

thats right! Now please explain

Answer 23

yipee !

Answer 24

well @ganeshie8 is correct !
but i have a different reasoning

Answer 25

oh..what is it?

Answer 26

We know that,
Interference of two wave can be written as :-
\[\large \bf I=I_1+I_2+2\sqrt{I_1I_2}\cos \phi \]

Answer 27

yes

Answer 28

Case 1 :- When coherent
since for coherent source,`phi` doesn't matter at all.
For max intensity, cos phi=1
So,
\[\large \bf I_{\max}=I_1+I_2+2\sqrt{I_1I_2}=(\sqrt I_1 +\sqrt I_2)^2\]
For `n waves`,
\[\large \bf I_{\max}=(\sqrt I_1+\sqrt I_2 + .....)^2=(n \sqrt I_0)^2=n^2 I_0\]

Answer 29

similarly apply for incoherent source

Answer 30

the second case is what i am doubtful in..

Answer 31

okay

Answer 32

Case 2 :- Incoherent Source
since `phi` depends.
So for `n waves` we take average ,
\[\large \bf <\cos \phi>=0\]
\[\large \bf I=I_1+I_2\]
for `n waves`,
\[\large \bf I=I_1+I_2+.........=n I_0\]

Answer 33

now take ratio,you'll get `n`

Answer 34

oh nice! Thanks!

Answer 35

no problem :)

Answer 36

THUMBS UP :D @ganeshie8

Answer 37

Nice!

Answer 38

<3

Answer 39

Thanks all!

Answer 40

yw :)