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Question
Answer the following question.
Write the conditions on path difference under which (i) constructive (ii) destructive interference occur in Young's double-slit experiment.
Solution
`I_1` = intensity of light from slit 1
`I_2` = intensity of light from slit 2
phase difference between 2 light waves = `theta = (2xΔx)/lambda`, where `Δx` = path difference resultant intensity `I` is given by,
`I = I_1 + I_2 + 2sqrt(I_1I_2) cos theta`
for constructive interference `I` should by maximum ⇒ `theta = 1`
`theta = 2npi, n = "Integer"`
`2npi = (2piΔx)/lambda`
`Δx = nlambda`
for distructive interference `I` should by minimum ⇒ `cos theta = -1`
`theta = (2n + 1)pi , n = "Integer"`
`2npi = ((2n+1)piΔx)/lambda`
`Δx = ((2n+1)lambda)/2`
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