The bottom of it that is, if somehow someone could be standing at the deepest point of the earths oceans how powerful would a torch pointed at the surface need to be to be visible from a boat above?
Thankfully do not need answer fast.
A side-question, unlike the top of Everest its hard to have a specific point to measure as to the very deepest part of the trench, what sort of resolution do they have for that?
I’ve tried reading the wikipedia on the Challenger Deep but its a little technical.
According to the NOAA, sunlight is occasionally barely detectable down to about 1000 meters.
Since Challenger Deep is ~10,000 meters, you’d need to handle that attenuation factor 10 times.
So, (brightness of the sun at the surface / minimum detectable brightness) ^ 10 times as bright as the sun.
Plus some, since detecting light at the surface with all the other light pollution is going to be harder than detecting the faintest light in almost total darkness down below.
At 100 meters, about 99.5% of light has been absorbed. The Challenger Deep is about 11 km deep, so the remaining light there is 0.005^(11000/100) = 8*10[sup]-254[/sup].
That is an absurdly small number–way smaller than the minimum energy that’s ever been measured compared to the mass-energy of the entire universe.
It’s actually even worse than that due to scattering. Even if you could put that amount of energy into, say, a laser beam, the light will be scattered far before it reaches the surface. You would end up illuminating the entire local region of ocean, not just a tight beam.
It would take way less energy to just lift the water out of the way and have a straight shot through air.
The photic zone is 200m, but the NOAA says 1000m until midnight. Challenger Deep is 10,900m or 10.9x deeper. So if we assume that the ocean water is the same throughout (dubious for many reasons), we can apply Lambert’s law and say we need 10.9 more light. Sunlight hits the ocean surface at illuminance of approximately 98 000 lux (lumens per square meter) on a perpendicular surface at sea level. such that we will need 98,000 lux* 10.9 = 1,070,000 lux. But if we assume that we just point a straight line between the surface and the bottom and if we assume a 1 cm**2 LED bulb, we just need a 107 lumens to make it to the bottom. But that seems absurdly small. But I’ve never dealt with lumens myself before.
Don’t you require Beer’s Law which states that the intensity of an electromagnetic wave penetrating a material falls off exponentially with distance from the surface?
Edit: interesting link on light absorption in water.
To quote Einstein: The greatest shortcoming of the human race is our inability to understand that exponential decay will make you its bitch.
One thing may be surprising to some–99.5% absorption seems like a lot. Wouldn’t everything be totally black at even 100 meters?
Surprisingly, no. The dynamic range of the eye is very high. A full moon is only 1/400,000 as bright as sunlight, and we can easily make our way around in that light. You would get to those levels at around 250 meters. But of course you can see to some degree even in starlight, which is around 100 times dimmer yet. That puts us down to 330 meters.
This is a very interesting question. Perhaps we can rig it a little bit. What was the most powerful torch ever built? If we put it on the bottom of the Mariana Trench, how far up would it still be visible? Would a submarine on, let’s say, 5000 m depth would be able to see it?
With the risk of derailing the thread…I worked on printing plate exposure machines with a 5 kW power metal-halide lamps. I have no idea how much is that in lumens though.
Didn’t see this thread until now. The answers given are right, though – exponential losses kill off the light. as for lasers, they’re highly directional and very bright, which is why the Navy has long funded research into blue-green lasers (the wavelengths most penetrating in ocean water) for communications (here’s an example: Blue-Green Laser for Undersea Communication ). They don’t tell you how far it can be used at its utmost (classified, I’ll bet), but they talk about communication over 10 km here: http://sea-technology.com/features/2011/0511/laser_communication.php
As for how many lumens in 5 kW, you need more information. Lumens are a measure of luminous flux (luminous energy per unit time), and luminous energy means energy spectrally weighted by the response of the human eye (so ultraviolet and infrared wavelengths aren’t counted, nom matter how large a contribution they make). You can’t convert between them unless you know the spectral makeup of the light.
[urlhttps://www.google.com/?gws_rd=ssl#q=metal+halide+lumens+per+watt]75-100 lumens per watt, so you’re dealing with somewhere close to 500,000 lumens.