- #1
MadMartigan
- 7
- 2
Homework Statement
So, my physics professor has been behind all semester long and basically taught the entire light wave and optics chapters in a single day and explained absolutely nothing, hence massive confusion on the following problem:[In a double-slit experiment, the slit separation is 1.75 mm, and two coherent wavelengths of light, 425 nm and 510 nm, illuminate the slits. At what angle from the centerline on either side of the central maximum will a bright fringe from one pattern first coincide with a bright fringe from the other pattern?]
d (split separation) = 1.75 mm = 1.75E-3m
λ1 = 425 nm = 425E-9m
λ2 = 510 nm = 510E-9m
θ = ?
Homework Equations
ΔX = dsinθ
dsinθ = mλ
The Attempt at a Solution
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Now, I think it's a constructive interference since the question references the bright fringes, not that I think that necessarily matters.
I've tried working this a few different ways and I honestly don't know if I'm on the right track since my professor spent of all 5 minutes on this and just spat out the equations he gave us on the board.
My first thought was to just use ΔX = dsinθ and plug and chug using path length difference.
510nm-425nm = 1.75E-3m*sinθ
Which would result in a tiny angle of 2.78E-3° which seems super small and has me questioning if I've screwed up.
And if I use the 2nd equation and add the wavelengths and have m=1, I get an angle of 0.031°. Small, but larger.
Am I on the right track on either of these methods or am I missing a concept entirely because my professor didn't explain jack?