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Approximately what is the smallest detail observable with a microscope that uses ultraviolet light of frequency $1.20 \times 10^{15} \mathrm{Hz} ?$

$\lambda=25 \times 10^{-8} \mathrm{m}$

00:52

Salamat A.

Physics 102 Electricity and Magnetism

Chapter 24

Electromagnetic Waves

Cornell University

Hope College

University of Winnipeg

McMaster University

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Okay, so we have a problem where we need to use the relationship between wavelength wave, speed and frequency. In this case, we are, um, given our frequency. And we asked about what? The smallest observable thing that uses, uh, electromagnetic radiation of that frequency could expect to see. So again, what is approximately, what is the smallest detail observed ball from a microscope that uses ultraviolet light. So ultraviolet light that we're using has a frequency of 1.2 times 10 of the 15 hurt hurts. Um, and we want to see what we would could see in a microscope using this. Well, what we would expect that we wouldn't expect to be able to see anything that was smaller than a wavelength of this light. So we have a wavelength here. So if we have a particle here that's smaller than the wavelength, we wouldn't necessarily expect the wave to bounce off of it. Um, and you know, so that we could then detect the reflected light and, you know, try to see the object so you can basically use as a kind of a rough estimate that you won't be. You certainly won't be able to see anything less than the wavelength of the light. Um, with any great detail. Anyway, obviously, some of the waves might bounce off. Some might not. But, you know, you're not gonna get a very good resolution. So what we can do then, is just use the relationship between wavelength, speed and frequency. And again, since it's electromagnetic radiation and there's wave, speed is the speed of light were given the frequency. So the wavelength is the speed of light divided by the frequency. And we see that we get a pretty small wavelength. Two points, 2.5 times, 10 to the minus seven meters. So that's, um, you know, that's what is that? 25 25 micron. Um, so you would probably not? Um no, that's that's not 25 micron. That is 0 to 5 microns. Um, you wouldn't expect this? Probably see much below one migrant with this microscope just because, you know, again, um, you want you want the wavelength particle, whatever you're looking at to, you know, be somewhat bigger than the wavelength of the light that you're using to look at it. So you wouldn't really see much, probably with any good detail. Um, any particle, anything that was above one micron. Um, because when you have a wavelength of 0.25 micron, yes, stand.

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