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$\bullet$$\bullet$ Resolution of the eye, II. The maximum resolution of theeye depends on the diameter of the opening of the pupil (a dif-fraction effect) and the size of the retinal cells, as illustrated inproblem 51 in Chapter $25 .$ In that problem, we saw that thesize of the retinal cells (about 5.0$\mu \mathrm{m}$ in diameter) limits thesize of an object at the near point $(25 \mathrm{cm})$ of the eye to a heightof about 50$\mu \mathrm{m}$ . (To get a reasonable estimate without havingto go through complicated calculations, we shall ignore theeffect of the fluid in the eye.) (a) Given that the diameter of thehuman pupil is about 2.0 $\mathrm{mm}$ , does the Rayleigh criterionallow us to resolve a 50 -\mum-tall object at 25 $\mathrm{cm}$ from the eyewith light of wavelength 550 $\mathrm{nm} ?$ (b) According to theRayleigh criterion, what is the shortest object we could resolveat the 25 $\mathrm{cm}$ near point with light of wavelength 550 $\mathrm{nm}$ ?(c) What angle would the object in part (b) subtend at the eye?Express your answer in minutes $\left(60 \mathrm{min}=1^{\circ}\right),$ and compareit with the experimental value of about 1 min. (d) Which effectis more important in limiting the resolution of our eyes, dif-fraction or the size of the retinal cells?

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a) So according to the Rayleigh criterion, we cannot resolve a particle of a height less than 84$\mu m$The Rayleigh criterion will $[$ not allow $]$ us to resolve a 50$\mu m$ tall object at 25 $cm.$b) 84$\mu m$c) This is greater than the experimental value of 1 min.d) A minimum angle subtended at the eye, by the diffraction pattern, is more when compared to the experimental value. Therefore, diffraction will have a greater effect in limiting the resolution of our own eyes.

Physics 102 Electricity and Magnetism

Physics 103

Chapter 26

Interference and Diffraction

Electromagnetic Waves

Reflection and Refraction of Light

Rutgers, The State University of New Jersey

University of Washington

McMaster University

Lectures

02:30

In optics, ray optics is a geometric optics method that uses ray tracing to model the propagation of light through an optical system. As in all geometric optics methods, the ray optics model assumes that light travels in straight lines and that the index of refraction of the optical material remains constant throughout the system.

10:00

In optics, reflection is the change in direction of a wavefront at an interface between two different media so that the wavefront returns into the medium from which it originated. Common examples include the reflection of light, sound and water waves. The law of reflection says that for specular reflection the angle at which the wave is incident on the surface equals the angle at which it is reflected. Reflection may also be referred to as "mirror image" or "specular reflection". Refraction is the change in direction of a wave due to a change in its speed. The refractive index of a material is a measure of its ability to change the direction of a wave. A material with a higher refractive index will change the direction of a wave to a greater degree than a material with a lower refractive index. When a wave crosses the boundary between two materials with different refractive indices, part of the wave is refracted; that is, it changes direction. The ratio of the speeds of propagation of the two waves determines the angle of refraction, which is the angle between the direction of the incident and the refractive rays.

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Resolution of the Eye. The…

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Let's first figure out the angular size of the object. And so the angler size is going to be the height of the object. Yeah, which is that over the distance to the object, which is 25 centimeters or that many meters. And so this expresses the actual angular size from your perspective, and this is equal to 2.0 times 10 to the last four. That's in radiance. Now that we have that, let's figure out what the angular resolution of your eyes and so we can do this. Using release Criterion 1.22 times claimed over D flinging in Lambda, which is 5 50 times 10 to the minus nine Andy for your eye, which is two times 10 to the minus 30 meters. This gives 3.4 times 10. Tim lies for radiance. And so since data, which is the actual angular size of the object, is less than your resolution ability, you cannot resolve the object. You cannot resolve the object for part B. We want to figure out what size object we can resolve. And so to do this, we're going to take our resolution angle here. We're going to equate it to the height of the object or the distance of the object. And so why is equal to the resolution angle Times s and we know what s is s is still 25 centimeters and we know what the resolution. Inglis. We found it here. And so it's equal to 3.4 times 10 to the minus four radiance. And so this equals 8.5 times 10 to the minus third centimeters, which is equal to 85 microns. And so this is the size of the object that you can resolve with this resolving power here. And if you're 25 centimetres away from it now, Marcie, we want to figure out what the angle is of the resulting power. So in this case, data is equal to the resolving eagle because we're on the limit of what we can resolve here and again. This is 3.4 times 10 to the minus for and that's in radiance. But if you want degrees, you Khun, convert easily two degrees to get 20.19 degrees. And then the problem asked for this in minutes and 60 minutes. Aaron, one degree. So if you convert this two minutes you get, we'll play one Our commitments. I'll put arc minutes. The problem just puts minutes, but stark minutes, and this is very close toe 1.0, which is the experimental value. So that's the experimental value, and it's very close to it. Party asked. What's more important, the diffraction or the other effect of your eye and answers that the diffraction is more important. But in order to really see this, you have to investigate the problem that they referred to in this question. The problem is 51 and Chapter 25 which tells you a little bit more about the other effect. But if you investigate this a little more, you'll find that diffraction. The fraction is is more important. But again, it's hard to answer this question with just this question along. You have to really go back to Chapter 25. Problem 51. The diffraction is is more important, and that completes the problem

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