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A Young's double-slit experiment is performed using the de Broglie waves of fast electrons from an electron gun. The spacing between successive maxima (fringe width) decreases the most when:

1. the accelerating voltage in the electron gun is decreased
2. the accelerating voltage is increased and the screen-to-slit distance is decreased
3. the screen-to-slit distance is increased
4. the slit separation is decreased

Correct answer: the accelerating voltage is increased and the screen-to-slit distance is decreased

Solution

β = λD/d. The de Broglie wavelength λ ∝ 1/sqrt(V), so increasing V reduces λ. Decreasing D also reduces β. Doing both together gives the largest reduction in fringe spacing. Decreasing V increases λ (larger β), and increasing D increases β, so those go the wrong way.

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