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In a Young's double-slit setup, a monochromatic beam (wavelength lambda = 600 nm in vacuum) is incident at an angle theta with respect to the axis of the apparatus. A thin glass slab of thickness t and refractive index mu is placed in front of the lower slit S2. The point O on the screen is at the position where the zeroth-order bright fringe (zero phase difference) is observed. Which relation correctly describes this condition?

1. (mu - 1) * t = d * sin(theta)
2. (mu - 1) * t = d * cos(theta)
3. mu * t = d * theta
4. t / (mu - 1) = d / sin(theta)

Correct answer: (mu - 1) * t = d * sin(theta)

Solution

For the zeroth-order fringe at O, the total optical path difference must be zero. The oblique beam creates a geometric path difference of d * sin(theta) favouring one slit; the glass slab of thickness t and refractive index mu adds an extra optical path of (mu - 1) * t to the lower slit path. Setting these equal gives (mu - 1) * t = d * sin(theta).

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