A pinhole camera has length L and the pinhole has radius a. The spot on the opposite wall is assumed to have a spread equal to the sum of its geometrical spread and its diffraction spread. For incident wavelength λ, the spot has minimum size bₘᵢₙ when:
Options

Question

A pinhole camera has length L and the pinhole has radius a. The spot on the opposite wall is assumed to have a spread equal to the sum of its geometrical spread and its diffraction spread. For incident wavelength λ, the spot has minimum size bₘᵢₙ when:

Options

G1 Physics · Accepted Answer

In the model used in the question, the geometrical spread is proportional to a and the diffraction spread is λL/a, so b=a+λL/a. For minimum spot size, db/da=1−λL/a²=0, hence a²=λL and a=√(λL). Then bₘᵢₙ=√(λL)+λL/√(λL)=2√(λL)=√(4λL). Therefore option D.