How far from some grains of red sand must you be so that you are just at the limit of resolving the grains if your pupil diameter is 3mm, the grains are spherical with radius 50μm, and the light from the gains has wavelength 650nm? If the grains were blue and the light from them had wavelength 400nm instead, would the answer to (a) be larger or smaller? Now let's say you are a superhero and you had x-ray vision, so you could see light that had a wavelength of 0.1nm instead. Now how far could you be from the gains of sand to just be at the limit to distinguish one grain of sand from another? (with the same pupil diameter). (assume you're on the beach and there's plenty of light from many
How far from some grains of red sand must you be so that you are just at the limit of resolving the grains if your pupil diameter is 3mm, the grains are spherical with radius 50μm, and the light from the gains has wavelength 650nm? If the grains were blue and the light from them had wavelength 400nm instead, would the answer to (a) be larger or smaller? Now let's say you are a superhero and you had x-ray vision, so you could see light that had a wavelength of 0.1nm instead. Now how far could you be from the gains of sand to just be at the limit to distinguish one grain of sand from another? (with the same pupil diameter). (assume you're on the beach and there's plenty of light from many
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Transcribed Image Text:(a) How far from some grains of red sand must you be so that you are just at the limit of
resolving the grains if your pupil diameter is 3mm, the grains are spherical with radius
50μm, and the light from the gains has wavelength 650nm?
(b) If the grains were blue and the light from them had wavelength 400nm instead, would
the answer to (a) be larger or smaller?
(c) Now let's say you are a superhero and you had x-ray vision, so you could see light that
had a wavelength of 0.1nm instead. Now how far could you be from the gains of sand
to just be at the limit to distinguish one grain of sand from another? (with the same
pupil diameter). (assume you're on the beach and there's plenty of light from many
frequencies bouncing off the sand, and when you turn on your x-ray vision you aren't
bothered by all the other frequencies around).
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