A camera's close-up lens is aimed at a butterfly 200 mmmm in front of the lens, creating a focused image on the detector 50 mmmm behind the lens. A proper exposure requires an f-number of F4.5F4.5.Part AWhat is the correct diameter of the lens aperture?
Question
A camera's close-up lens is aimed at a butterfly 200 mmmm in front of the lens, creating a focused image on the detector 50 mmmm behind the lens. A proper exposure requires an f-number of F4.5F4.5.Part AWhat is the correct diameter of the lens aperture?
Solution
The f-number (also known as the focal ratio, f-ratio, or relative aperture) of an optical system is the ratio of the lens's focal length to the diameter of the entrance pupil. It is a dimensionless number that is a quantitative measure of lens speed, and an important concept in photography.
The formula to calculate the diameter of the lens aperture is:
Diameter = Focal length / f-number
Given that the focal length is the distance from the lens to the image sensor when the subject is in focus, in this case, the sum of the distances in front and behind the lens, which is 200mm + 50mm = 250mm.
And the f-number is given as 4.5.
So, substituting these values into the formula, we get:
Diameter = 250mm / 4.5 ≈ 55.56mm
So, the correct diameter of the lens aperture should be approximately 55.56mm.
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