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Light of wavelength λ is incident on a slit of width d. The resulting diffraction pattern is observed on a screen placed at a distance D from the slit. If the linear width of the central maximum equals the width of the slit, then D=

Asked in GUJCET 2015 · Single slit diffraction

• (1) (2d²)/λ
• (2) (d²)/(2λ)
• (3) d/λ
• (4) (d²)/λ

Step-by-step solution

Why the other options are wrong

• (1) Moves the 2 to the wrong side. From (2λ D)/d=d you divide by 2λ; multiplying by it instead gives (2d²)/λ, four times too large.
• (3) A length divided by a length is a pure number, so d/λ cannot be a screen distance at all -- a useful check on any answer of this shape.
• (4) Uses the half-width (λ D)/d as the whole central maximum. The central maximum runs from the first minimum on one side to the first minimum on the other, so it is twice that.

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