A Young's double-slit experiment has a usable screen extending from −12 mm to +12 mm. Initially the fringe width is 2 mm. The screen distance is then doubled without changing wavelength or slit separation. How many bright fringes that were initially visible are no longer visible after the change?
Physics · Wave Optics · young's dubble slit experiments
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Question

A Young's double-slit experiment has a usable screen extending from −12 mm to +12 mm. Initially the fringe width is 2 mm. The screen distance is then doubled without changing wavelength or slit separation. How many bright fringes that were initially visible are no longer visible after the change?

Physics · Wave Optics · young's dubble slit experiments

G1 Physics · Accepted Answer

Initially, β₁ = 2 mm. The visible bright orders satisfy |m|×2 ≤ 12, so |m| ≤ 6. Thus 13 bright fringes are initially visible. When D doubles, β₂ = 4 mm. Now, |m|×4 ≤ 12 gives |m| ≤ 3, so only 7 bright fringes remain. Therefore, lost bright fringes = 13−7 = 6. Hence the answer is 6.