Question

The normal lens on a 35-mm camera has a focal length of 50.0 mm Its aperture diameter varies from a maximum of 18 mm (f /2.8) to a minimum of 2.3 mm (f /22). Part A Determine the resolution limit set by diffraction for f/2.8. Specify as the number of lines per millimeter resolved on the film. Take A = 560 nm Express your answer using two significant figures: lines mm RP( f /2.8) Submit Request Answer Part B Determine the resolution limit set by diffraction for f/22. Specify as the number of lines per millimeter resolved on the film. Take A = 560 nm Express your answer using two significant figures: lines mm RP( f /22)

Answer 1

The resolution limit by diffraction for a camera lens with an f/2.8 aperture is approximately 6.3 lines per mm. This is calculated using the formula for the diffraction limit in terms of numerical aperture and wavelength of light.

Step-by-step explanation:

The student's question relates to the resolution limit set by diffraction in optics, more specifically in a 35-mm camera lens at different aperture settings. To determine the resolution limit set by diffraction, we can use the formula for the diffraction limit R = 1/(2NA), where NA is the numerical aperture of the lens, and for a camera lens, NA is given by NA = aperture diameter / (2 × focal length). At an aperture setting of f/2.8 with a maximum aperture diameter of 18 mm, the numerical aperture (NA) is 18 / (2 × 50.0 mm) = 0.18. The resolution power (RP), or the number of lines per millimeter, that can be resolved by the lens, is then inversely proportional to the Rayleigh criterion, which can be calculated using RP = 1/(λ / (2 × NA)), with λ being the wavelength of light, taken as 560 nm (0.560 μm).

For f/2.8: RP(f/2.8) = 1/(0.560 mm / (2 × 0.18)) which approximately equals 6.3 lines per millimeter.

For f/22, with a minimum aperture diameter of 2.3 mm, the calculation would follow similarly, resulting in a different resolution limit.