Question

optimum sharpness of one image occurs when the diameter of the central maximum equals the diameter of the pinhole. what is the optimum hole size for a pinhole camera in which the film is 20 cm behind the hole? assume 550 nm , an average value for visible light.

Answer 1

The optimal pinhole diameter for a pinhole camera with film 20 cm behind the hole, assuming a light wavelength of 550 nm, is calculated using the Rayleigh criterion formula resulting in an approximate diameter of 0.55 mm.

Step-by-step explanation:

The student is asking about the optimal hole size for a pinhole camera with the film placed 20 cm behind the hole and assuming an average wavelength of 550 nm for visible light. The question relates to the diffraction pattern created by a circular aperture and the Rayleigh criterion for resolution.

To find the diameter of the optimal pinhole, we use the formula θ = 1.22 λ/D, where θ is the angle to the first diffraction minimum, λ is the wavelength of the light and D is the diameter of the pinhole. The question suggests that the optimum sharpness of an image occurs when the diameter of the central maximum equals the diameter of the pinhole.

Applying the Rayleigh criterion and substituting the given values, we have:

D = 1.22 × 550 nm × (20 cm) / D, solving this equation yields D ≈ 0.55 mm as the optimal diameter for the pinhole.