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In a two-slit interference pattern, the intensity at the peak of the central maximum is I0. (a) At a point in the pattern where the phase difference between the waves from the two slits is 60.0°, what is the intensity? (b) What is the path difference for480-nm light from the two slits at a point where the phase difference is role="math" localid="1663934638478" 60.0°?

Short Answer

Expert verified
  1. The intensity is 0.75I0.
  2. The path difference from the two slits is 80nm.

Step by step solution

01

Formulas used to solve the question

Intensity is given by

I=I0cos2(ϕ2)

Phase difference is given by

ϕ=r*2πλ

02

Calculate the intensity

Given: ϕ=60°=π3rad

λ=480nm=480*10-9m

Now, the intensity is given by

I=I0cos2(ϕ2)

Plug the given,

I=I0cos2(602)=0.75I0

03

Calculate the path difference

From equation (2), solve forr

r=λϕ2π

Plug the given,

r=480*10-9*π32π=8.0*10-8m=80nm

Thus, the intensity is 0.75I0. The path difference from the two slits is 80nm.

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