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In a Young's double-slit setup, a thin glass sheet of refractive index mu and thickness t is placed in front of the lower slit S2. The line from the slits to the screen makes angle theta with the central axis. For the central bright fringe to appear at point O on the screen, the condition is:

1. (mu - 1)*t = d*sin(theta)
2. (mu - 1)*t = d*cos(theta)
3. (mu - 1)*t + d*sin(theta) = 0
4. t/(mu - 1) = d/sin(theta)

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

Solution

Inserting the sheet adds an extra optical path (mu-1)*t to the lower slit's beam. For the zero-order (central) maximum at O, the net path difference between the two beams must be zero. The geometric path difference for the given direction is d*sin(theta). Balancing the two gives (mu-1)*t = d*sin(theta).

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