In a standard YDSE two slits are covered by a wedge shape film of refractive index $μ$ as shown in the figure. The thickness of film varies linearly from t to 3t from one end as shown in the figure. The distance between the two slits is d. The screen is at distance D from slits. Monochromatic light is used in experiment. Choose the correct option(s): (d<<D)

Select correct alternative(s)

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If the film is displaced $\frac{d}{2}$ along +y axis the central maxima will shift away from O

If the film is displaced $\frac{d}{2}$ along -y axis the central maxima will shift away from O

Central maxima is formed at distance $\frac{2 t (μ - 1) D}{3 d}$ below O

If the film is displaced $\frac{d}{2}$ along + y axis the fringe width will remain same

answer is A, D.

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Detailed Solution

Shift in fringe pattern
$= \frac{t_{2} (μ - 1)}{λ} β - \frac{t_{1} (μ - 1)}{λ} β$ $= \frac{(t_{2} - t_{1}) (μ - 1) β}{λ}$
$= \frac{d \tan θ (μ - 1) β}{λ}$ (constant) $= \frac{2 t (μ - 1) D}{3 d}$

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