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In a Young's double slit experiment, the upper slit S1 is covered by a glass plate of refractive index 4/3 and thickness 9*lambda, while the lower slit S2 is covered by a glass plate of refractive index 3/2 and thickness 2*lambda (lambda = wavelength of light used). If I0 is the intensity due to each slit individually at point P (the central position without plates), which of the following statements is/are correct?

1. The intensity at point P is 4*I0.
2. Two fringes shift in the upward direction after inserting both glass plates.
3. The optical path difference between waves from S1 and S2 at point P is 2*lambda.
4. If the source S is shifted upward by a small distance d2, the fringe (originally at P after plate insertion) shifts downward by D*(d2/d1).

Correct answer: The optical path difference between waves from S1 and S2 at point P is 2*lambda.

Solution

Extra optical path through upper plate (S1): delta1 = (4/3 - 1)*9*lambda = (1/3)*9*lambda = 3*lambda. Extra optical path through lower plate (S2): delta2 = (3/2 - 1)*2*lambda = (1/2)*2*lambda = lambda. Net path difference at central point P = delta1 - delta2 = 3*lambda - lambda = 2*lambda. Since the path difference is 2*lambda (an even multiple of lambda), it corresponds to constructive interference — intensity = 4*I0. But constructive means bright fringe, and 2*lambda path difference means the bright fringe has shifted — by 2 fringe widths. Since extra path is added to S1 (upper), the fringe pattern shifts upward by 2 fringes (toward S1). So: Option A (intensity 4*I0) — TRUE (constructive interference). Option B (2 fringes shifted upward) — TRUE. Option C (path diff = 2*lambda) — TRUE. Option D (source shift upward by d2 causes downward shift of D*d2/d1) — TRUE (standard result: source shift and fringe shift are in opposite directions).

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