Alien creature sends (emails) us a selfie from its home planet (about which we know very little). Is it possible to determine how tall it is from the photo itself?
Would it help or not if we can make a single request regarding the photo composition?
Do we know the location of the home planet? If so, the easiest option might be to have the being take its picture outside with some astral body (like its sun) clearly visible, then we could do some napkin math to get a very rough ballpark figure, comparing what we know about the relative distances of the astral body and the surface of the planet. It would be even better if we knew at what time it was taken so we know about how close the planet is to the astral body at the time and such to narrow down the results.
To do so would require a common unit of length. Since you alien may have a different light source, that would be no use, so IMHO it would simply not be possible.
If you could make a single request you could ask to have the selfie taken in front of the antenna used to transmit the image. We would know the frequency, therefore the wavelength and the alien’s size could be determined in that way.
Not entirely unrelated, but the human line drawings on the Pioneer plaque use the probe itself as a reference to give the size of humans.
What if it poses next to a dripping wet surface? Water droplets are all roughly the same size, that would give us a standard of comparison.
Just make sure we specify that it’s wet with water, just in case they think “wet” means “hose it down with sulfuric acid”.
I forget, is it 6 qudlots to a freeth, or is it 16?
Is this true for different atmospheric pressures, compositions and conditions? We shouldn’t assume the alien planet is Earth-like, with Earth’s surface gravity, etc.
Wouldn’t work. We might know how big their sun is and how far away their planet is, but that just gives us the angular size of their sun. That would in turn let us determine the angular size of everything else in the picture, including the alien… But the angular size of the alien will depend on both the alien’s actual size and the distance of the camera. Assuming that aliens take selfies the same way we do, by holding the camera at arm’s (or tentacle’s) length, all we would be able to tell would be the ratio of the creature’s height (or other dimensions) to its appendage length (which we could probably get anyway).
With some appropriate (or not) assumptions, though, we might still be able to get something. If we know the wavelengths of light used, and if we assume that their cameras have diffraction-limited optics, and if their sensor resolution is high enough to be insignificant, then we could use the resolution to determine the aperture of the camera. If we then further assume that they design the cameras to have approximately the same aperture as their eyes, then we could use the eyes to scale the rest of the image. That’s a lot of assumptions, though.
I think the best option would be DJ Motorbike’s suggestion to include the transmitting antenna in the photo. There are other ways you could get even more information, but they’d require diagrams and other information you’d only expect from a scientist trying to specifically communicate that information.
sand. have the alien acquire the finest sand it could and pour it around, playing with it and picking out a single grain for us to see.
or use a banana for scale
Assuming we could explain the concept of a Mole, we could ask the alien to pose alongside (say) a stack of molar iron cubes
Unlikely. Our own concept of a mole is based around the gram, which is earth specific.
ETA: Oh, if we explained it to them ahead of time. If we could communicate concepts like that, we could always just give them the definition of a meter and of a second to give them something to measure length.
Just have them pose next to a quarter, like we do with spiders and stuff. 
Or just ask them how long it takes light to traverse the length of their body. We all have at least that one measuring stick in common.
If we have a unit of time in common with them, at least.
What unit would that be? Planck length?
The meter had a standard definition: “1,650,763.73 wavelengths of the orange-red emission line in the electromagnetic spectrum of the krypton-86 atom in a vacuum.” That’s been supplanted,* but should be close enough. It does not require any knowledge of human measurement units. You could show them an image of the krypton spectrum with the correct line marked (if you can see their image, they can see yours, and this would work if you could send a B&W image)
Of course, you don’t need to be precise. If it’s off by a foot, it should be good enough to give you an idea.
*The current definition uses the second as a measure of time, which means it wouldn’t work for aliens.
You’re right. :smack: To be fair I was just thinking out loud, trying to be productive after my stupid joke.
Though if we knew where in the universe they are, perhaps we could ask them to measure themselves in fractions of the distance between our planet and theirs. They’d have to have a rough idea, since they sent us the picture.
The second used to be defined by the number of vibrations of a particular cesium isotope at a certain temperature. If we had a common measure of temperature (say, a star both our worlds could see and study), that might work.
Of course, now a second is defined by how long it takes light to travel a certain distance, so that wouldn’t help with the aliens either.
True, but by using the old Kr-86 definition, you don’t have any problems.
Kr-86 is Kr-86, and the number of wavelengths is a number that doesn’t require any other reference. Designating the correct line doesn’t even require a knowledge of our terms for color if you can send them a photo of the spectrum with an arrow pointing to it. Since the meter stick doesn’t have to be precise, you can even round off the number of wavelengths.