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University of Wisconsin - Milwaukee

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Problem 44 Medium Difficulty

(a) Calculate the limiting angle of resolution for the eye, assuming a pupil diameter of 2.00 mm, a wavelength of 500 nm in air, and an index of refraction for the eye of 1.33. (b) What is the maximum distance from the eye at which two points separated by 1.00 cm could be resolved?

Answer

a. 2.29 \times 10^{-4} \mathrm{rad}
b. 43.6 m

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Video Transcript

So here people diameter of the eye as two millimeter. The Web linked off light and air is 500 nanometer and refractive index of the eye is 1.33 So in part A to find the limiting angle off resolution, the web link off light in the eyes would be them die because lambda over an So this term here actually comes straight from the definition of the refractive index. Okay, so this is actually Lambda over. And I so remember, refractive index is the ratio of the velocity of light in vacuum to the rescue of the velocity off light in this case and I So from their velocities frequency times, web linked and frequency is gonna be constant in both mediums. So we just end up with the web link here. Okay, So now to find there a minimum, we're just going to use 1.22 Lambda Chi over D and Lambda. I is going to chance to the 1.22 Lambda over and I time STI. Now we have the web length given, which is Lambda is just lambda air and an eyes given these the diameter. So if you plug in the value of everything in here. You're going to get 2.29 times 10 to the negative Floridian. So this is are valid for that? That I mean, for part a now to solve part B lis skirt of the different page. So what we're gonna do in Part two is we're gonna find the maximum distance from the eye at which two points separated by s the separation between the two points, which is ass equals one centimeter. We're gonna find the distance between this object and observer. All right, so let's write this down. In terms of meter, we're going to do the same thing to use the definition for that, I mean, in this case is going to be s over. Our, as is the separation between the two objects and R is the distance between the observer and the object. And this is going to give us our egos as over. They're mean. We know the value of the ketamine from part, eh? So it's going to be a syrah prince here. One over 2.29 times 10 to the negative for pretty in, and this will give us 43.7 meter

University of Wisconsin - Milwaukee
Top Physics 103 Educators
Elyse G.

Cornell University

LB
Liev B.

Numerade Educator

Marshall S.

University of Washington

Farnaz M.

Other Schools