What is the smallest object or length that we could possibly actually see?

Ergroilnin · 2ヶ月前

I'm excited to see the paper!

Ergroilnin · 2ヶ月前

Doh. I meant lower frequency stuff. Will update post.

Ergroilnin · 2ヶ月前

Brain. I double checked the numbers and formulas, because its been a long time since I used them.

BoRamShote · 2ヶ月前

Yes. The world has almost 21 billion chickens, according to the United Nations Food and Agriculture Organization: http://faostat3.fao.org/home/E

Ergroilnin · 2ヶ月前

It's time to bust out the Abbe limit. Back in the 19th century, this was a hot question (for obvious reasons: people wanted to build better microscopes). Guys like Helmholtz, Abbe, and Zeiss were all working on this problem.

The resolution of an optical microscope is limited by two things: the numerical aperture (which is determined by the lens) and the wavelength of the light involved in seeing.

The Abbe formula, defining the resolving limit of the microscope is

d = λ / (2a), where λ is the wavelength of the light, d is the resolution limit, and a stands for aperture. Aperture is defined as n sin θ, where n is the refractive index of the material you're looking through, and θ is the half-angle of the biggest cone of light that can come into the lens.

So if you build a microscope with a bigger aperture, you can see smaller stuff. There are tradeoffs though, like you limit your depth of field.

Anyway, if we use special immersion oil instead of air, there's a maximum numerical aperture of about 1.5, assuming we are able to build a lens that captures just about all the light coming off the object.

So let's go back to the Abbe limit.

d = λ / (2a)

d = λ / (2*1.5)

d = λ / 3

Let's use violet light at 380 nm, since it's the shortest light we can see.

d = 380 nm / 3 = 126 nanometers.

So that's our theoretical maximum optical resolution. In reality, you're not going to get there. You're going to have a lower aperture, and you're going to have lens flaws, and all kinds of other issues. Plus you're going to want to use lower frequency light to see some stuff.

Way more information about real-world microscopes can be found here: http://micro.magnet.fsu.edu/primer/anatomy/numaperture.html

DigitalSterling · 2ヶ月前

About 1380 meters, assuming we use Lawrence Livermore's new petawatt pulsing laser, and assuming no scattering or vaporizing (that's a huge assumption).

You can do the math yourself!

Use the modified Lambert equation up there. Plug in 1 PW in milliwatts (since you have the input and you want the output of 1 mW). Plug in whatever coefficient you like from the paper. Solve for d.

DigitalSterling · 2ヶ月前

Please refer to the link in my last edit. Look up the wavelength you want. Red laser has a wavelength of about 650. The higher the absorption coefficient in the table, the more power will be needed. You'll see that red is far from the best choice in this scenario.

DigitalSterling · 2ヶ月前

It is impossible for a laser beam to penetrate 11,000 meters of water, yes.

DigitalSterling · 2ヶ月前

Yes, considerably. It changes the absorption coefficient of the seawater. Which changes the answer hugely... but the power requirements are still unimaginable. Read my final edit.

DigitalSterling · 2ヶ月前

M in the paper's Table 2 is a measurement of different types of seawater.

However, 7%/m is still well within the range of reasonability. Proof follows:

As we've determined, 10³⁴⁴ is the input power assuming absorption of 7% per meter.

Thus, we can reformulate the linear version of Lambert's law as follows:

10³⁴⁴ = e^a*11000 . Solving for a, the absorption coefficient reveals that a is approximately equal to 0.072.

Referring to Table 2 in the linked paper, we can find coefficients in that range (and higher) in every type of ocean water across a variety of wavelengths. The original question did not specify wavelength. Thus, my original answer, while considerably higher than the power required for "pure" seawater, is representative of many real-world values.

DigitalSterling · 2ヶ月前

Shoot, that's a way better seawater coeff than I found. So it takes way less power than my math indicates... but it's still literally astronomical.

DigitalSterling · 2ヶ月前

Yeah, it's many many multiples of the mass-energy equivalent of the universe, according to wolfram alpha. So I guess your laser would be briefly visible before everything disappeared.

DigitalSterling · 2ヶ月前

Yes. The 7% is best-case.*

You can see the rate of absorption changing as you descend through the water column when scuba diving. Reds go first, followed by the rest of the colors in sequence. By not-very-deep, you need a flashlight to see anything at all.

*In the real-world seawater samples tested by the scientists.

DigitalSterling · 2ヶ月前

Yeah, it's going to be insane. I just am not sure enough what the heat mechanics are there (in terms of -how fast- the water would vaporize) to feel confident in any math I'd do.

DigitalSterling · 2ヶ月前

Ok so. Seawater absorption is complicated and depends on lots of things (contents of water, wavelength, etc). There's a paper that suggests about 7% per meter under relatively ideal conditions.

So multiplying that over the depth of the Mariana trench, you come out with loss such that to get 5 mW of power to the bottom of the trench, you need 1.5 x 10³⁴⁴ W of power at the surface. Which is too much. I haven't done the math to see just how much of the ocean you'd be vaporizing at that point.

EDIT: By "too much" I really meant "more than all the power." That amount of power is many many many multiples of the sun's power. It's more than all the possible power.

EDIT 2: Please look below for other calculations based on different coefficients of absorption. It makes a huge difference... but only in the sense that the answers range from "more power than the universe is equivalent to" to "only a few hundred times more than the luminous intensity of the entire galaxy". So in a practical sense the answers are the same, though they are wildly different.

EDIT 3: I've gotten some messages about coefficients of absorption. Basically different parts of the ocean absorb water differently. The coefficient of absorption of seawater ranges from about 0.013 to... whatever you want it to be, really. The wavelength matters a whole lot. The 7%/meter answer I got was an average based on white light in real-world pelagic seawater. With real-world seawater your answer ranges from roughly 10⁶⁰ watts to 10³⁵⁰ watts for lasers of optimum sea-water penetration. Get out of that wavelength and the power skyrockets. EVEN SO. Whether you're talking about 10⁶⁰ or 10¹⁴⁷ or even a fraction of that... you're talking about unimaginable amounts of power. Power such that the universe cannot supply.

If you want to try it yourself, x=e^ad is a supersimplified version of the equation (Lambert's), where x is the input power, a is the coefficient of absorption and d is the depth in meters. That'll give you the number of input units needed to get one output unit. This paper has a bunch of science and a table on the absorption rates.

spider999222 · 2ヶ月前

Great question.

This paper attempts to answer this very question. They concluded that there is no definite evidence that rabies was present in humans in pre-Columbian America, but there is circumstantial evidence of bat rabies.

This_Old_House · 8ヶ月前

In New England back in ye olde days, it wasn't uncommon to put a petrified cat in the wall as a protection from evil!

foretopsail · 1年前

What's more outrageous are all these questions about dinosaurs on an archaeology unit. This is why archaeologists only ever get asked about dinosaurs, which we don't even know anything about. :(

LoTekk · 1年前

You'll have better luck over at http://www.reddit.com/r/whatisthisthing

jakeizaak · 1年前

Dang, I copy/pasted the wrong thing. I meant to paste these two. This question comes up a lot, so forgive me for being quick on the remove button.

http://www.wired.com/2014/02/think-yellowstone-erupt/

http://www.reddit.com/r/askscience/wiki/planetary_sciences/yellowstone

If those don't answer your question, or you have a followup question, absolutely feel free to post a new askscience question!

Hope that helps.

jakeizaak · 1年前

http://www.reddit.com/r/askscience/comments/1x6tae/what_is_really_happening_right_now_in_yellowstone/

foretopsail · 1年前

This is an insanely large topic.

There is no way you'll get a grant to do a comprehensive study of religion, superstitions, and beliefs from ancient to modern, and their role in history and modern society. Waaaayyyyy too big.

Think of the question you want to answer. Make sure it's a single sentence with a question mark at the end. Then ask yourself what you'd need to know to answer that question. Make those things into sub-questions, each with question marks. Pick the smallest sub-sub question you can answer, and figure out how you'd answer that. Apply for the grant to answer that question.

Also, the size of the grant matters a lot. Is this a big grant from a government with a multi-million dollar budget? Is this a tiny little $1,000 thing from a local foundation? Do you have other funding? The answer to that will dramatically alter the questions you can answer.

Finally, it sounds like you're a student. It also sounds like you have a lot of introductory reading you should do in all of these fields. Many grants want to see that you're at a point where you can make a substantive contribution to the field. To do that, you really need to know what the state of the field is at the moment.

CapableLover · 1年前

Arr! The Flying Dutchman!

CapableLover · 1年前

Woof! Truman!

Edit: I'm definitely curious to see who the 'correct' answer is. It's hard to say who the first left-handed President is, but Truman definitely was, according to David McCullough.

youarefeelingsleepy · 1年前

In archaeology, big projects are almost always written up in book form. So we read a lot of those!

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