While moving an object between a light source and a clean mirror surface, its shadow seems hardly visible (at least compared with a non reflecting surface).
Is it correct that the shadow is not visible ?
How do you explain this behavior ?
[Physics] Are shadows cast on mirror surfaces
opticsvisible-light
Related Solutions
After appending my 2019-04-30 update to my much older answer, the above excellent, to-the-point and from-the-trenches expert answer came in. I immediately changed the designated answer from mine to the new one. There's probably still some fun reading below in my old reply and update, though... :)
Alas, I must answer my own question: I found a very explicit example online description of someone who created a thick-film transmission hologram of a convex mirror. She (or he) describes seeing her own face clearly, even if only in monochrome. So, if I accept this description at face value, it clearly is possible to create a realistic mirror using only wave-exclusion diffraction effects. Cool!
Also, I am amused (or is it chagrined?) that this reminded me of the importance of reading long articles all the way to the end, even if you feel you already got the point. This description of an actual holographic mirror was hidden at the very end of the long posting on I mentioned in my question about how transmission holograms cannot form mirrors.
2019-04-30 Update
As noted in the comments below, the above link to an explicit description of a holographic mirror unfortunately is no longer available, not even in Internet archives.
However, this draft book chapter PDF on reflection using Denisyuk transmission holograms seems to provide pretty good coverage of the issues.
Still, as I get older I find I like finding the simplest possible explanations of things. The simplest proof that true holograhic mirrors can exist is this: You can see your own face in a pool of calm water.
Why? Well, the reason why thick film holograms can reflect light at all is because any change in refractive index in a transparent medium creates an amplitude -- a probability -- for light to be reflected back in the direction in which it came. Metal mirrors are just extreme examples of this effect, since the Fermi surface electrons in metals create a nearly 100% probability that photons will be reflected.
The quantum mechanical details of reflections works in transparent materials are covered delightfully in my favorite Richard Feynman book, QED: The Strange Theory of Light and Matter. In addition to its relevance here for understanding what is possible with holograms, I recommend QED strongly to anyone interested in understanding just how utterly and completely weird quantum mechanics really is.
Feynman discusses how properly space layers of changes in refractive index can create a surface that, at least for certain frequencies, has a nearly 100% probability of reflecting light. A holographic mirror!
Finally, take a contemplative look at this image (or a real example from your kitchen) of a roll of very layers of Mylar film:
Nearly everyone has at sometime noticed at some level of consciousness how remarkably metallic such rolls look, almost like aluminum foil. That is because even though the distances between the film layers are not wave-coherent as they would in a photographic hologram, they do collectively reflect more and more light, until the surface looks remarkably metallic... which is to say, remarkably like a mirror.
Such a roll of Mylar film thus can plausibly be construed as a crude mechanically constructed hologram, and thus a proof that at least at some level of quality, transparent materials can indeed be configured to create plausibly effective, metallic-looking reflective mirrors.
Refraction has nothing to do with the effect.
There is a very straightforward explanation of this effect in terms of simple geometric optics, and the simple observation that the size of physical sources of light is always larger than zero, compared to mathematically ideal point-source.
A diagram is probably worth a 1,000 words of explanation here:
Edit in reply to comment: Physically, a yellow object in shadow will be perceived as the same color because a shadow is the absence of light as opposed to black light. So you merely see less yellow instead of a mixture of yellow and black. To reproduce the effect of shadows in paintings, you have to mix black pigment with the color pigment of the object you're shading. But by adding black to yellow you've inadvertently shifted the yellow hue in the greenish-blue direction (see the first image you provided in your question). Painters solve this problem by mixing in pigments which shift the hue in the complementary direction (in this case purplish-red), and the idea is that two shifts of cancel out to yellow again.
This is why painting is hard. The optics is easy though, and it should be emphasized that this part of your question belongs to color theory. The subtlety here is of paints, not optics.
Best Answer
Everything you see that does not emit light itself is due to light from an external light source being scattered. Most objects scatter light in all directions, so no matter where you position yourself, you will see the object. If something blocks the light from the source, less light will be reflected from a particular area. This area is the shadow. Since light may come from several sources (e.g. light scattered several times in the sky), the shadow usually doesn't appear completely black.
Shadows are cast on mirror surfaces. But a mirror only reflects light in one direction, so to see the shadow you have to position yourself at a very special place, namely the place where you see the light source in the mirror. Again, if there are other light sources, the shadow won't appear black, and since parallel light rays remain parallel after hitting the mirror, you will in fact see a mirror image of the shadowing object.
The figure below may help explain. Solid lines are sunrays, dashed lines are where there would be sunrays if there hadn't been blocked by the tree. If you lay a mirror in the shadow of a tree, you'll have to place yourself exactly where the line extended between the sun and the tree, extended to the mirror and out by the same angle, hits your eyes.