Interference Wave Equation

[elemis]

1. The problem statement, all variables and given/known data

2. Relevant equations

In question.

3. The attempt at a solution

To be clear it's part (vi) that's unclear to me.

In order to ignore the cosine term it has to reduce to 1. This can happen, only if k(x₁+x₂)/2 = ωt

Is this a correct assumption ?

Also, it is known that k = 2∏/λ and ω=2∏/T

However, I'm trying to think in what way these two components could be equal but I can't get it.

Could someone give me some help, please ?

[Mr Diamond]

I do not think that your assumption is correct, because the question is not about cosine reduced to one.

In order to find the answer, you have to ask your self "what kind of effect does cos[k(x₁+x₂)/2 - ωt] have after long exposure of the light on the plate?"

[swansont]

"Long exposure" being a key phrase.

[elemis]

I'm guessing we have to consider the time average of cosine ? Can you help me a bit more ?

"Long exposure" being a key phrase.

 

 

I do not think that your assumption is correct, because the question is not about cosine reduced to one.

In order to find the answer, you have to ask your self "what kind of effect does cos[k(x₁+x₂)/2 - ωt] have after long exposure of the light on the plate?"

 

I'm guessing we consider the time average of Cosine ? CAn you help me out a bit more ?

[swansont]

Not a time average of cosine— that would be zero. Detectors don't measure wave amplitudes, they measure intensities, which is the square of the wave amplitude.

 

Do cameras measure time averages?

[elemis]

Not a time average of cosine— that would be zero. Detectors don't measure wave amplitudes, they measure intensities, which is the square of the wave amplitude.

 

Do cameras measure time averages?

Could you please be a bit more explicit ?

[swansont]

Answer the question — do cameras measure time average of the light falling on them, or is it some other function? (Think about whether you can overexpose a shot)