Comments on: Energy conservation in interference of light? http://www.energy--talk.com/alternative-energy/energy-conservation-in-interference-of-light/117/ How Can We Be More Energy Efficient? Thu, 17 May 2012 11:58:22 +0000 http://wordpress.org/?v=2.6.5 By: Somu http://www.energy--talk.com/alternative-energy/energy-conservation-in-interference-of-light/117/#comment-212 Somu Mon, 10 Dec 2007 09:27:34 +0000 http://www.energy--talk.com/alternative-energy/energy-conservation-in-interference-of-light/117/#comment-212 Let E1 = amplitude of first wave, E2 = amplitude of second wave Then total energy before inteference = 1/2 E1^2 + 1/2 E2^2 = 1/2 (E1^2 + E2^2) Total energy after interference = 1/2 (E1+E2)^2 = 1/2 (E1^2 + E2^2 + 2E1E2) 1/2 (E1^2 + E2^2) + E1E2 So E1E2 is extra. This is what you are talking. Right? Here is the explanation. E1 and E2 are vectors. So, in place of E1E2 you should take E1.E2 which means dot product of E1 and E2. There are constructive and destructive interferences. When the waves meet, then in some places the dot product is positive and other places negative so that when you add all of them, then total value of the dot product becomes zero. Thus energy is conserved. Let E1 = amplitude of first wave,
E2 = amplitude of second wave
Then total energy before inteference = 1/2 E1^2 + 1/2 E2^2
= 1/2 (E1^2 + E2^2)
Total energy after interference = 1/2 (E1+E2)^2
= 1/2 (E1^2 + E2^2 + 2E1E2)
1/2 (E1^2 + E2^2) + E1E2
So E1E2 is extra. This is what you are talking. Right?

Here is the explanation.
E1 and E2 are vectors. So, in place of E1E2 you should take
E1.E2 which means dot product of E1 and E2. There are constructive and destructive interferences. When the waves meet, then in some places the dot product is positive and other places negative so that when you add all of them, then total value of the dot product becomes zero.
Thus energy is conserved.

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