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The box of a pin hole camera, of length L, has a hole of radius a. It is assumed that when the hole is illuminated by a parallel beam of light of wavelength λ the spread of the spot (obtained on the opposite wall of the camera) is the sum of its geometrical spread and the spread due to diffraction. The spot would then have its minimum size (say b_min) when:

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

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

Solution

The correct option relates the radius of the pinhole to the wavelength and length of the camera in a way that minimizes the diffraction spread, achieving the smallest possible spot size on the opposite wall. This relationship is derived from the principles of optics, where the geometrical and diffraction effects combine to determine the minimum spot size.

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