The intensity I of the light reaching the CCD in a camera is proportional to the area of the lens. Because this area is proportional to the square of the diameter D, it follows that I is also proportional to D2. Because the area of the image is proportional to q2 and q ≈ f (when p >>f , so p can be approximated as infinite), we conclude that the intensity is also proportional to 1/f2 and therefore that I ∞ D2/f2. The ratio f/D is called the f-number of a lens. Therefore, I ∞ 1/(f-number)2. The f-number is often given as a description of the lens’s “speed.” The lower the f-number, the wider the aperture and the higher the rate at which energy from the light exposes the CCD; therefore, a lens with a low f-number is a “fast” lens. The conventional notation for an f-number is “ f/” followed by the actual number. For example, “ f/4” means an f-number of 4; it does not mean to divide f by 4! Suppose the lens of a digital camera has a focal length of 55 mm and a speed of f/1.8. The correct exposure time for this speed under certain conditions is known to be 1/500 s. (a) Determine the diameter of the lens. (b) Calculate the correct exposure time if the f-number is changed to f/4 under the same lighting conditions.
The intensity I of the light reaching the CCD in a camera is proportional to the area of the lens. Because this area is proportional to the square of the diameter D, it follows that I is also proportional to D2. Because the area of the image is proportional to q2 and q ≈ f (when p >>f , so p can be approximated as infinite), we conclude that the intensity is also proportional to 1/f2 and therefore that I ∞ D2/f2. The ratio f/D is called the f-number of a lens. Therefore, I ∞ 1/(f-number)2. The f-number is often given as a description of the lens’s “speed.” The lower the f-number, the wider the aperture and the higher the rate at which energy from the light exposes the CCD; therefore, a lens with a low f-number is a “fast” lens. The conventional notation for an f-number is “ f/” followed by the actual number. For example, “ f/4” means an f-number of 4; it does not mean to divide f by 4! Suppose the lens of a digital camera has a focal length of 55 mm and a speed of f/1.8. The correct exposure time for this speed under certain conditions is known to be 1/500 s. (a) Determine the diameter of the lens. (b) Calculate the correct exposure time if the f-number is changed to f/4 under the same lighting conditions.
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