Verified answer

They can. People do it all the time. There is no issue with autofocus and mirrors.

If the image looks blurred it is probably because the photographer was shaking his or her hand too much.

The maximum temperature that can be achieved by focusing the rays from any source is the temperature of the source itself. Since the surface of the sun is about 5778° K, that's the theoretical limit of what can be generated in a solar collector. It's one of the interesting problems of optics to prove that using ordinary (and passive) lens and mirrors, one cannot make any visible object "brighter" to the eye. This is why night vision goggles require active light amplication. However, there is an easier thermodynamic reasoning why this should be true. Suppose it is possible by such passive means to generate a temperature which is greater than some source. Then we would be able to achieve 100% efficiency from any thermodynamic machine using a heat source, because any waste heat it generates could then be "cranked back up" to the temperature of the original heat source. This violates one of the basic findings of thermodynamics, where the efficiency of any machine is determined by the temperature of both the hot and cold sinks. I'm giving this one a star because it was one of my favorite puzzlers a while back, and it still has a lot of interest to me today. Addendum: Remo, the proof in optics depends on the fact that sun (or anything else) isn't a point object. For simple systems, like a single lens or mirror, it suffices to show that the fact that magnification is equal to the ratio of distances of the object and image to the objective. The real challenge is proving it for any and ALL possible optical systems. What about non-linear optics, or use of what's now called "meta-materials"? That was one of the problems I puzzled over at one time when I was in college. I was thinking of ways of achieving light amplication before the days of active night vision systems. remember.kelly has given the basic proof, but it is not an exhaustive one. What fascinated me about this question is that an question in OPTICS should have a bearing on THERMODYNAMICS (and vice versa). It's one of those intriguing connections that pop up regularly in physics, and makes you want to think there's something much deeper going on. This is one example why I can't help but find physics and the mathematics of it so engrossing. Addendum 2: Deep Sky Blue, I believe it was Robert Hooke who showed centuries ago that for paraxial optical systems, energy flux is a constant. So, a "series of lens" still won't do the job. You'd have to be more clever than that. Also, thermodynamic efficiency of ANY machine goes up with greater temperature differences. This is exactly the reason why geothermal sources of power as well as ocean thermoclines tend to be marginal providers, except at exceptional locations. Addendum 3: Thanks, remember.kelly, for that more generalized proof. It's a more rigorous version than showing that magnification is equal to the ratio ot distances as I said above, and it's in line with Hooke's original reasoning. However, even this proof does depend on an idealization of light, and for this reason it is still not the last word. But, you definitely deserve the 10 points here for bringing up the subject of poincare invariants. I've saved that for my own files.

They can. It's no problem whatsoever.

Just put the focus point in the viewfinder on the camera, and not the person holding it.

Peace.

Most of the time it's just because of poor aim. Auto focus need to be able to "see" something to focus on.