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For path difference λ, phase difference = 2π rad. For path difference λ/4, phase difference = π/2 rad. As K = 4I₀, calculate the intensity at a given point where path difference is λ/4.

1. K' = K
2. K' = K/2
3. K' = K/4
4. K' = K/8

Correct answer: K' = K/2

Solution

The intensity at a point in an interference pattern is given by I = I₀(1 + cos(Δφ)), where Δφ is the phase difference. For a path difference of λ/4, the phase difference is π/2, and cos(π/2) = 0. Substituting, we get I = I₀, so K' = K/2.

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