Diffraction angle minimized by larger wavelength-to-gap ratio inverse

Steps:

• Recall diffraction angle θ ≈ λ / a for small angles in single-slit diffraction.
• Note wavelength λ = v / f, with wave speed v constant, so θ ≈ v / (f a).
• Smallest θ requires maximizing product f × a.
• Compute products: A gives (f/2)(a/2) = fa/4; B gives (f/2)(2a) = fa; C gives (2f)(a/2) = fa; D gives (2f)(2a) = 4fa.

Why D is correct:

• D maximizes f × a (to 4fa), minimizing θ per θ ≈ v / (f a) formula.

Why the others are wrong:

• A: Minimizes f × a (to fa/4), maximizing θ.
• B: Yields f × a = fa, larger θ than D.
• C: Yields f × a = fa, larger θ than D.

Final answer: D