(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Two isotropic point sources of light (s1 and s2) are separated by 2.7micrometers along a y axis and emit in phase at wavelength 900 nm and at the same amplitude. A point detector is located at point P at coordinate Xp on the x axis (s1 is also on the x axis, at (0,0).) What is the greatest value of Xp at which the detected light is minimum due to destructive interference?

I don't know how to make a diagram for this on the computer but say there is an x,y plane: S1 is on the origin, P is at distance Xp to the right of S1 (on the X axis) and S2 is at 2.7um from S2 (lower, on the Y axis.)

2. Relevant equations

Y = (λL (m+½)) / d

Where Y is the position of the interference minima

L is the distance Xp

D is the slit space (2.7 um)

and λ is the wavelength.

m= mode.

1.[itex] d\sin\theta=m\lambda[/itex] for constructive interference

2.[itex]d\sin\theta=(m+\frac{1}{2})\lambda[/itex] for destructive interference

3.[itex]\phi=\frac{2\pi}{\lambda}(r_2-r_1)[/itex] phase difference related to path difference

3. The attempt at a solution

I figure since the center of interference is always between the two slits (or in this case point sources), y = 1/2 of 2.7um, i.e. 1.35 micrometers, and thus

Y = (λL (m+½)) / d

1.35 x 10 ^- 6 = [ (900 * 10^-9) * L (m+½) / 2.7 * 10 ^ 0.6 ]

or

4.05 x 10 ^ -6 = L (m+½).

And I'm stuck there, I don't know if I'm to suppose that m is 0 seeing as how that would give the biggest L.

The answer is 7.88 x 10^-6 m, but I can't get it...

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# Light: interference - two slit

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