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A pinhole camera has a box of length L, and the pinhole has radius a. If a parallel beam of monochromatic light of wavelength λ falls on the hole, the image spot formed on the opposite screen is taken to have a total spread equal to the sum of the geometrical blur and the diffraction blur. Under this assumption, the spot attains its least size bmin when:

1. a = √(λL) and bmin = √(4λL)
2. a = λ² / L and bmin = √(4λL)
3. a = (2λ² / L) and bmin = (2λ² / L)
4. a = √(λL) and bmin = (2λ² / L)

Correct answer: a = √(λL) and bmin = √(4λL)

Solution

Total spread b = a + lambda*L/a (geometric + diffraction). db/da = 1 - lambda*L/a^2 = 0 gives a = sqrt(lambda*L), and bmin = 2*sqrt(lambda*L) = sqrt(4*lambda*L).

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