Finding the minimas from EM radiation.

[sg001]

Homework Statement

6. S1 and S2 in the diagram are effective
point sources of radiation, excited by
the same oscillator. They are coherent
and in phase with each other. Placed 4.0 y m apart, they emit equal amounts of
power in the form of 1.0 m wavelength electromagnetic waves.
(a) Find the positions of the first (that is, the nearest), the second, and the third maxima of the received signal, as the detector is moved out along axis OX.
(b) Is the intensity at the nearest minimum equal to zero? Justify your answer.
[Ans: (a) 7/6m, 3m, 7.5m; (b) No]


the diagram looks like this


^y
|
|
|
|*S2
|
|
|
|
|
O*S1______________________>X
where d is the distance between S1 and S2

Homework Equations

The Attempt at a Solution

(a)
let dx = the distance along the x-axis to the respective minima.

so sin θ = d/√(dx²+d²)

for maxima's

dsinθ=mλ

for m=0 (the first maxima)

dsinθ = 0

so x =1 -d²

x =√15 m

but this is wrong but I'm not sure where I have gone wrong.. it should be 7/6 m

for m=0.

 

[ehild]

This is not the same situation as with a slit, interference of the diffracted waves.

You have two different waves from different sources.
What is the condition of constructive interference when two waves meet? ehild

 

[sg001]

This is not the same situation as with a slit, interference of the diffracted waves.

You have two different waves from different sources.
What is the condition of constructive interference when two waves meet?


ehild

ok so use 2nt = mλ

 

[sg001]

that they are in phase...

so x=mλ

 

[skeptic2]

What is your reasoning behind your answer for (b) No?

 

[ehild]

that they are in phase...

so x=mλ

Yes, a single wave has minima and maxima, but we speak about constructive interference of two waves. You said that the waves must be in phase. That is not quite true. The phase difference between them has to be integer multiple of 2pi. That corresponds an optical path difference nt=kλ, where n is the refractive index of the medium, t is the path difference, and k is an integer.
Supposing we have constructive interference on the x-axis at a point x. What is the path difference between the rays from the two sources when they reach x?

ehild