Two isotropic point sources of light (s1 and s2) are separated by 2.7 mm along a

Question

Two isotropic point sources of light (s1 and s2) are separated by 2.7 mm 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

a) What is the greatest value of Xp at which the detected light is minimum due to destructive interference?

b) If the detector at P is moved to the right along the x-axis from source S1, at what distances from S1 are the first three intereference maxiuma detected?

please please legible soultions please with explainations!!! and usage of pictures thank you!

Explanation / Answer

Destructive interference occurs when the phase difference is exactly (an odd multiple of) pi radians. This corresponds to length difference of half the wavelength. You need to find a point where the difference between the distance to S1 and S2 is exactly half the wavelength. The waves also destructively interfere at 3/2 the wavelenght, 5/2 the wavelength... but these occur closer to the origin.

The distance to S1 is simply x
The distance to S2 derives from the pythagorean theorem: sqrt(x^2+y^2). y is given.

sqrt(x2+y2)-x=w / 2
sqrt(x2+y2)=w / 2+x
x2+y2=(w/2+x)2
x2+y2=w2/4+2wx/2+x2
y2=w2/4+wx
wx=y2-w2/4
x=(y2-(w/2)^2)/w
x=(27002-4502) / 900
x~=7875
7875 nm=7.875 um

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