Most animals—humans included—have eyes that use lenses to form images. The eyes of scallops are different. A typical scallop eye forms images largely by reflection from a mirror- like surface at the back of the eye. as shown the important features of a typical scallop eye. The lens causes very little redirection of incoming light rays; it is the spherical surface in the back of the eye that brings rays of light to a focus on the cells of the retina. (For simplicity, we’ve shown no refraction by the lens, although the lens does cause some refraction that seems to help to make the image sharper by correcting for the spherical aberration introduced by the mirror.) The reflection is due to thin-film interference from the front and back faces of 80-nm-thick transparent crystals of guanine, index n = 1.83, that are embedded in cytoplasm with index n = 1.34. The individualeyes are quite small. A typical scallop has 40 to 60 eyes, each with a 450-mm–diameter pupil and a reflecting surface at the back of the eye with a focal length of only 200 mm. The unusual imaging system of the scallop eye makes it very sensitive to light. The ratio of the focal length to the aperture of an optical system is known as the f-number. A smaller f-number implies greater light sensitivity. A telescope optimized for light gathering might have an f-number of 4; the scallop’s f-number of less than 0.5 means that its small eyes work well in very dim light. For the typical pupil diameter of 3.0 mm, what is the approximate f-number for a human eye?A. 2B. 4C. 6D. 8

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Most animals—humans included—have eyes that use lenses to form images. The eyes of scallops are different. A typical scallop eye forms images largely by reflection from a mirror- like surface at the back of the eye. as shown the important features of a typical scallop eye. The lens causes very little redirection of incoming light rays; it is the spherical surface in the back of the eye that brings rays of light to a focus on the cells of the retina. (For simplicity, we’ve shown no refraction by the lens, although the lens does cause some refraction that seems to help to make the image sharper by correcting for the spherical aberration introduced by the mirror.) The reflection is due to thin-film interference from the front and back faces of 80-nm-thick transparent crystals of guanine, index n = 1.83, that are embedded in cytoplasm with index n = 1.34. The individual
eyes are quite small. A typical scallop has 40 to 60 eyes, each with a 450-mm–diameter pupil and a reflecting surface at the back of the eye with a focal length of only 200 mm. The unusual imaging system of the scallop eye makes it very sensitive to light. The ratio of the focal length to the aperture of an optical system is known as the f-number. A smaller f-number implies greater light sensitivity. A telescope optimized for light gathering might have an f-number of 4; the scallop’s f-number of less than 0.5 means that its small eyes work well in very dim light.

For the typical pupil diameter of 3.0 mm, what is the approximate f-number for a human eye?
A. 2
B. 4
C. 6
D. 8

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