Suppose that you can barely resolve two red dots because of diffraction by the pupil of your eye. If we increase the general illumination around you so that your pupil decreases in diameter, does the resolvability of the dots improve or diminish? (You can assume that only diffraction is important here.)
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The resolution of an optical system (like the eye) is determined by its diffraction limit, which is related to the size of the aperture (in this case, the pupil). Show more…
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$\bullet$$\bullet$ Resolution of the eye, I. Even if the lenses of our eyes functioned perfectly, our vision would still be limited due to diffraction of light at the pupil. Using Rayleigh's criterion, what is the smallest object a person can see clearly at his near point of 25.0 $\mathrm{cm}$ with a pupil 2.00 $\mathrm{mm}$ in diameter and light of wavelength 550 $\mathrm{nm}$ ? (To get a reasonable estimate without having to go through complicated calculations, we'll ignore the effect of the fluid in the eye.) Based upon your answer, does it seem that diffraction plays a significant role in limiting our visual acuity?
Even if the lenses of our eyes functioned perfectly, our vision would still be limited due to diffraction of light at the pupil. Using Rayleigh's criterion, what is the smallest separation between two pointlike objects that a person could clearly resolve at his near point of $25.0 \mathrm{~cm}$ with a pupil diameter of 2.00 $\mathrm{mm} ?$ Assume that the light has a wavelength of $550 \mathrm{nm}$. (To get a reasonable estimate without having to go through complicated calculations, we'll ignore the effect of the fluid in the eye.) Based on your answer, does it seem that diffraction plays a significant role in limiting our visual acuity?
The normal human eye has maximum visual acuity with a pupil size of about $3 \mathrm{mm}$. For larger pupils, acuity decreases due to increasing aberrations; for smaller pupils, acuity decreases due to the increasing effects of diffraction. If your pupil diameter is $2.0 \mathrm{mm},$ as it would be in fairly bright light, what is the smallest-diameter circle that you can barely see as a circle, rather than just a dot, if the circle is at your near point, $25 \mathrm{cm}$ from your eye. Assume that the light's wavelength in air is $600 \mathrm{nm}$ and the index of refraction inside the eye is 1.33.
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