Irene asked in Science & MathematicsPhysics · 1 month ago

# State the difference in the distances, from each slit to point Y?

How to find it? Thanks

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• Anonymous
1 month ago

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• NCS
Lv 7
1 month ago

For the first dark fringe, d*sinΘ = λ/2

0.41mm * sinΘ = 580e-6mm / 2

sinΘ = 7.07e-4 → Θ = 0.04053º

tanΘ = 2.0mm / D

D = 2.0mm / tan0.04053º = 2827.5855 mm (around 2.8 m)

top slit:

D' = √(2827.5855² + (2.0 - 0.41/2)²) mm = 2827.5861 mm

bottom slit:

D" = √(2827.5855² + (2.0 + 0.41/2)²) mm = 2827.58636 mm

Note that the calculated path length difference is around 260 nm; it should be ½*580nm = 290 nm. I suspect that the difference is due to the "rounding" of some of the measurements given. But it's also possible I've made a math error.