To take a good self-portrait, I'd look in the mirror, see the expression/angle/light I like, and... fail to capture it.
Any tips on exposure, positioning of the camera (e.g. relative to the eyes), focal length/lens to use.
What it boils down to:
I am not talking about photographing through the mirror. The mirror is only a tool here.
The angle captured by the human eye is essentially equivalent to a normal lens. What defines the focal length of a normal lens will differ based on your camera. On a 35mm camera, this would be a 50mm lens; on the more common digital cameras with cropped sensors, you would shoot for somewhere in the 28-35mm range.
The eye has an iris. Although the mechanism is a bit different from your lens, the effect is not unlike the aperture in your lens. You can observe how the aperture responds to changes in lighting conditions by observing how pupils dilate when going from a brighter space to a darker one and constrict when making the reverse transition.
So assuming your mirror is indoors, you might choose a relatively wide aperture to match your eye's. Perhaps it's my nearsightedness, but looking around the room right now, my eye seems to have a DOF roughly equivalent to something in the 4.0-5.6 range.
The eye, like a digital sensor, has variable sensitivity. I would push the ISO up to around 800-1600 to get the exposure you need.
When viewing a subject through a mirror, the distance is always greater than the distance from you to that subject directly. More precisely, it is the distance from the observer to the mirror plus the distance from the mirror to the subject. In the case where you are looking at yourself in the mirror, it is twice the distance from you to the mirror. So, in other words, if you are 2 feet from the mirror, your reflection will appear 4 feet away.
Needless to say, when you are looking in the mirror, you are at eye level, and pretty much head-on. A photo that mimics this would likewise be taken straight-on.
When you are looking at the mirror, you are presumably using only available light. This may be some light through the window, or one or more lamps, perhaps. To get the same effect you would want to have similar light sources at similar angles with respect to the subject. Importantly, this precludes use of an on-camera flash.
What I've outlined here is some answers to the types of questions you are asking--specifically regarding the technical aspects of what you see in a mirror. This may be an interesting project, but it may not be the same approach you would take if your goal was to get a great self-portrait. A more interesting self-portrait might not be head-on at eye-level. Whereas the lighting in your mirror-portrait would be as-is, you might instead choose a lighting configuration set up specifically for the photo. The point is that this is strictly a technical discussion of reproducing what you see in the mirror, and may not be the "best" self-portrait you can accomplish. On the other hand, it might be a fine starting point.
Actually, I think that this is much less about the technical settings and the camera equivalent of the human eye — which, by the way, is covered in this earlier question, and this one as well — and more about some actually somewhat heady questions of identity and self-perception, as well as a more mundane but still philosophical issue of the difference between fluid motion in time and a frozen frame.
There's some degree where, if you want a certain look, you'll need to replicate the lighting and technical factors that match your mirror setup. You'll probably want to start with a lens with a "normal" focal length — that is, a little less than 50mm-equivalent — somewhere around 28-35mm on an APS-C camera.
But, here's an important thing. Your mirror provides a 1:1 representation. Are you going to print at that size? Maybe if we're talking about a hand mirror, the answer is yes, but if not, suddenly you're working with a very different perception of "normal". That means, you might actually get better-feeling results with a longer focal length. (In general, I think printing so that you are life-size is an important aspect of getting a true mirror feel, if that's an important part of this project; even if you might end up cropping very heavily as if looking in a small mirror.)
Beyond that, though, is one of the intrinsic issues in all of photography. When you're looking at real time — even if you're holding very still — little awkwardnesses and imperfections and so on appear less so than they can when captured in a still. The flicker of a smile which moves from the lips to the eyes and back can be powerful and subtle in real life — and totally missed in a photo. In fact, it can look really weird if caught in the wrong instant. When you're looking in the mirror in real life, millions of years of human development in recognizing these subtle cues is at work, and it goes directly to special centers in the brain dedicated to figuring it all out. With a photograph, you're cutting all of that out.
The best way to learn about this is to practice — the self-portrait skills here aren't particularly different from those in capturing expressions in portraits in general. Arranging your own expression in a mirror is something different, though, and I think the only answer really can be "practice, practice, practice". One important aspect, of course, is eye contact — you can't see yourself in a mirror without it, so make sure you're looking directly at the lens.
And of course, there's the issue that mirror-image people look slightly odd and different — if your friends were kidnapped in the night by aliens and returned inverted, you'd notice that something was off, even if you couldn't pin it down. But it's beyond that. If you stand next to a friend and look in a mirror, they'll see you very differently from the way you do, not because of the angle, but because our impression of human beings is complicated and not a matter of optics.
Vincent van Gogh painted dozens of self-portraits over his lifetime. I think it's safe to say that these represent his perception of himself in the mirror much more powerfully than a painting or photographic portrait someone else made ever could. I think these are probably very true to what he saw in the mirror, even if they are not always completely literal.
So, then, there's really a question. Do you want to do that — capture your inner perception of yourself for all to see? Or, is it really more hey, I kind of like what I see in the mirror, but I can't get it in a photograph? Know which of these you want to aim for will help a lot, but I think in either case, once you have a basic setup, the approach is to take a short series and immediately review the results (ideally, on a big screen, not just the camera's LCD — see the point above about the size of a mirror).
Examine the technical, and make adjustments to better match your desired results — watch the lighting and shadows particularly, and decide if the angle is right for your perception of your features in the mirror. Play around with size and cropping.
Most importantly though, watch your expression and the minutiae of minor differences in your posing. Does it look too stiff? Not angled right? Go back right away and do another series with those changes, and repeat. (This isn't a magic bullet solution, but there rarely is!)
The idea of using a half-mirror is an interesting one, and may help you get more direct results. Be aware, though, that the existence of one-way mirrors is a myth. There's just glass that's half reflective, and if you're in a well-lit room and the other side is dark, it's a mirror — while if you're in the dark room, you can see through into the light. It might help better with eye contact than the other approach of putting a mirror next to the camera and shifting slightly to look into the lens. I'd be interested to see your results with that approach.
Here is just one hypothetical setup that you can use:
Lets assume you have a mirror that you can move around. This is the mirror you use to look at yourself. Assume this mirror is made of a fairly solid frame from which you can easily remove the glass. (I personally assumed your mirror is about one meter tall, but that's just my imagination)
Position the mirror in the place where you look the way you want, but where you can put the camera on a tripod Behind the mirror at the very same height and at the same distance.
Arrange your lights, background, etc, the way you want. then, remove the mirror glass without moving the frame. Now go to your camera, which is positioned behind the mirror frame at the same height and distance from the back of the mirror as you where from the front. (The center of the lens should be at the same height as your eye was while you posed for the mirror. And if your face was at, say, one meter from the mirror, the camera should be a meter away from the back of the mirror. Use metering tape, long rulers or a suitable piece of rope to measure distances.
Zoom out fully until you see the four sides of the inner border of the mirror frame, then zoom in until the first side is just about to "get out of the picture". Set your timer or remote, go to pose and look trough the frame and to the camera. Voila! Then in post, crop the photo so you leave the mirror frame out.
This assumes the mirror you are looking yourself at, is perfectly vertical. The camera should be in the same spot relative to the frame as your head in order to conserve the composition you are seeing. This is, if you position yourself in front of the center of the mirror, then do so with the camera. If you put your head in the upper-left third of the mirror, the camera should be placed "in front" of the upper-right third of the back of the frame. Another way to say it is, when you see your left eye with your left eye through the mirror, the line of sight is completely perpendicular to the plane of the mirror, so, when you look at the camera through the empty frame, your line of sight to the camera lens should be absolutely perpendicular to the plane of the (now imaginary) mirror. You should see the camera looking straight at your eye!.
Getting it real: I know most of us don't have such a mirror, this is just a mental exercise made up to think about the relative position of the camera, the light sources and the subject. The reasoning behind this is based on:
The apparent distance between you and your reflection is the double of the distance between you and the mirror surface. (you can "wiki" this) The size of the mirror frame is somehow related to the focal length that should be used to take the picture with the same composition you see in front of the mirror. (I just don't want to do the math and it is not really necessary)
So, when you arrange your set up, you may not have the moveable mirror, just imagine it. You can easily make an aid that is a cardboard frame where the cutout has the dimensions of your mirror.
GO in front of your mirror and take note of the distances where you put yourself, where the light sources are. Draw schematic diagrams if that helps. Then, replicate the arrangement using the aid frame, then position the camera, etc... Remember that the frame is just an aid, I'm not pushing you to put the frame into you picture, zoom in a little bit so it does not appear in, but, the camera should be pointing straight at you in order to get the same perspective, so you may have to crop one, two or three sides of the picture in order co capture what you see.
And finally: if you just happen to have such mirror, arrange the whole setup, pose, and have someone move the mirror out just before the shoot!
Hope these ideas help. Regards.
Well... at least I didn't notice anyone point it out here, but mirrors very often do not give a perfect reproduction. It is not uncommon for them to warp a bit: http://www.apartmenttherapy.com/mirror-images-a-131365 Also, while unproven, it may very well be the case that some of them are slightly warped to be more flattering. The following article shows some good and bad cases, though they were not super careful about making the images with exactly the same framing:
To get the effect for your particular mirror, I suppose I would suggest busting out the grid paper and creating a distortion profile as you would for a lens. Additionally you could consider the effects on the reflected light, mirrors can shift that in different ways, which you can also see a bit in the shots in that article.
Eye level, pointed directly at the eyes/square, whatever distance you usually stand from the mirror, choose purely by the AOV for the framing you want but choose a lens with low optical distortion or that you have a good distortion profile for. The only optical distortion we want is whatever you measured form your mirror, applied separately, and the perspective distortion is determined purely by your distance, so by matching the distance earlier we have ensured that it is the same as you see in the mirror.
"What is the digital (optics, settings) equivalent of an eye?" This has been covered in many places, but I don't think it is actually critical to getting the result you're looking for. AOV is probably the biggest takeaway from it, but there is contention because at what point do we discount the periphery that we don't have real focus on? Possibly you could attempt to sort of simulate that by framing a bit wider but using a lens that is sharp in only the center 3/4ths or so then falls off in sharpness.