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University of Wisconsin - Milwaukee

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Problem 43 Medium Difficulty

To increase the resolving power of a microscope, the object and the objective are immersed in oil (n= 5 1.5). If the limiting angle of resolution without the oil is 0.60 mrad, what is the limiting angle of resolution with the oil? Hint: The oil changes the wavelength of the light.

Answer

0.40 \mu r a d

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Video Transcript

So in this problem, the refractive index of toilets given, which is what about five were also given that the limiting angle off resolution without oil is 0.6 micro Radian. We want to find out the limiting angle off resolution with oil being used. So to do that, we start with air. So let's find out the debt. I mean for the air, their relation for that. So they don't mean that a minimum for air is 1.2 to Lambda over D, and that one is given, which is 0.6 Michael Arad make a radiant. But so for the oil, then a minimum for the oil is going to be 1.22 Lambda Oil over D. So we don't know the wavelength of oil. But what we can do is we can use the definition of refractive index for the oil. So that is basically the rescue of the Web link delight in vacuum to webbing of the light in oil. So if we use that relationship and oil goes lambda Lambda Oil, we can actually replace that here in this relationship here and then we will get 1.2 to Lambda by D And instead of Lambda Oil being here, we're gonna put in oil because this is what is given. Great. So from here, we can go to next Peach. That, I mean for oil is going to be called to 0.6 times 10 to the negative six, which was one point to do. Lambda by D Times 1/1 0.51 point five is the refractive index of will. So this will give us here a point for times 10 to the negative six radiant or 0.4 micro Radian.

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

Cornell University

Andy C.

University of Michigan - Ann Arbor

Farnaz M.

Other Schools

Zachary M.

Hope College