Around 470 people voted in yesterday's optics quiz. I continue to be amazed at the power of radio button polls to bring people into the blog.
As of early Friday morning, the correct answer is solidly in he lead-- 63% of respondants have correctly replied that the image remains intact, but is half as bright. You can see this fairly easily by looking at a traditional ray diagram of the image-forming process (re-drawn slightly from yesterday's picture, to get the arrows right):
The arrows in this picture show the paths followed by three different rays of light that all leave from the tip of the arrow, and converge to form the tip of the arrow in the image. There are, of course, an infinite number of rays that all leave the arrow and converge at the tip, but these three mark out the extremes of the range. Rays that head out from the arrow above the top line shown, or below the bottom line shown, won't be bent strongly enough to make it to the image. Any ray between the top and bottom lines shown will end up in exactly the same place at the image.
As you can see, one of these three passes through the top half of the lens, one passes (more or less) through the center, and one passes through the bottom half. If you block one of these-- say, by putting the card over the bottom half of the lens, the other two (and the infinite number of other rays passing through the upper half) still make an image on the far side. So, the image from half a lens is the same as the image from the whole lens, just a little dimmer because of the missing rays of light.
There was a small amount of discussion in comments of whether the image on the far side appears blurry or not. This is due to the effect of diffraction-- the fact that the lens is a finite size imposes an upper limit on the amount of light that can pass through it, and this causes the waves to spread out a little. The amount of spreading increases as the lens gets smaller, which is why you want a really big lens (or mirror, or other optical element) if you want to look at small things far away (say, through a telescope or a telephoto lens). For this sort of scenario, though, the diffraction effect is pretty minimal-- the images when we do this in lab appear slightly less distinct, but that's a matter of lower contrast due to the increased intensity, rather than blurring due to diffraction.
So, there's your magic optics trick for the week. Time permitting later this morning, I will explain what this has to do with the Laser Smackdown.
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Thank goodness. I've never gotten so uptight about hitting a radio button before. I don't think my ego could have taken it had I gotten wrong a question from my first university physics course. :-) I guess I can breath again.
So why does nobody make a half-lens camera? It'd be awesomely stylish, space-efficient, cost-efficient (two cameras per lens!), and apparently it would still work.
I say this is nonsense, and the lack of half-lens products in the marketplace shows that your so-called "science" is all a sham.
Snappy answer: they do - they just remove the outside half.
Lots of reasons having to do with aberrations, coma, optical alignment and so on. Plus the ease of working with round bits rather than half-rounds.
Which I'm sure you knew. With mirrors rather than lenses, there are many applications where they in essence use a half-mirror, such as your home satellite TV dishes, which has the advantage keeping the feed horn from obscuring part of the dish. It also gives the dish better side to side directivity for the same aperture, which is important as there are other satellites using the same frequencies in geosynchronous orbit. Those dishes are diffraction-limited, so dimensions matter.