There's a lot of poor information out there regarding looking directly at the sun (or looking at it through a mirror). As a general rule-of-thumb, it's a bad idea to look directly at the sun, but that is very overstated and the effects that it has on the eye depend on some very clearly-defined factors.
It's not actually harmful to look at the sun briefly - otherwise every human (as well as all apes and probably many other mammals) would accidentally blind themselves during early childhood. But there are several different types of eye damage that can occur.
1: over-saturation of the receptors. This is the most common type of damage, and it is the bluish or greenish thing that appears in your vision whenever you look at the sun or any bright light for a few seconds, or after a camera flash. The small light receptor cells in the retina can only output a certain amount of signal when they receive light. If they receive too much or receive it for too long, they get a bit overloaded and need to rest (they're cells, they can only handle so much). You will tend to see a reversed 'afterimage' (like a photographic negative) while these cells refresh. This is generally regarded as harmless, though it's probably not a good idea to overload the cells frequently because that's simply not how they are supposed to be used. Some more information is in the first section at http://www.healthguidance.org/entry/9913/1/Spots-Dots-and-Floaters-Seeing-Whats-Inside-Your-Eyes.html
2: burning or extreme over-saturation of small portions of the eye. This is the primary concern with lasers. A bright small light can cause direct damage (not mere overuse, but outright damage) to small parts of the retina, either through radiation damage or by concentrating heat on a very small area. This WILL cause long-lasting damage; sometimes it can heal over weeks or months, but sometimes it can be permanent. However, it is only to a portion of the retina, so the eye will still work, but vision won't be as good, and it can create significant blindspots. A powerful laser can do this, and looking at the sun through binoculars or a telescope can also do this on a rather large portion of the retina.
3: burning of the entire retina - this is the type of damage that people worry about the most from the sun. If you stare at the sun with your naked eye for a long time (several minutes to several hours), you can overheat the entire retina and kill many of the cells just from the heat. As the eye is mostly water, and has blood vessels that circulate liquid, it is good at handling and dissipating heat. But it can only handle so much. Additional cells can also be killed by the UV radiation that the eye concentrates onto the retina - so those cells may die hours or days later in addition to the ones that were killed more quickly by the heat. Most of us have the instinctive reaction of not staring directly at the sun, so this isn't a problem, unless someone forces themselves to do it.
4: long-term UV damage. If you stare at the sun often, or are in a profession where you are often at very high altitudes (such as a pilot) where UV isn't filtered from sunlight as much, or often use a tanning bed without eye protection, then you can accumulate damage from gradual UV exposure. The UV damages the cells on the molecular level. This damage is very gradual and often isn't instantly noticeable, and sometimes isn't even felt until well after the event because the damage can be in forms that prevent cells from repairing or reproducing. This is a problem common among old career pilots from the era when cockpit windows didn't have anti-UV tinting. It also tends to tie into other vision-reducing problems, because it's radiation damage and basically radiation damage harms everything - hence it will make any other (or latent) problems worse.
For the sun, the real worry is from the last two cases. For your question, the panels don't focus light onto a tiny pinpoint, so you won't get any damage from the concentrated light. And the light travels through the atmosphere on its way down to you, so most of that UV radiation is filtered like normal, in addition to its the dispersion in the reflection. And the panels don't reflect nearly enough light to overheat any part of the retina.
So you CAN look at the sun, as long as you follow certain precautions: don't stare at it for a very long time (and especially don't hold it in the same part of your vision if you do), don't magnify the amount of light that your eye collects (like with a telescope or binoculars), don't concentrate that light down to a very small point, and don't look at it from very high in the atmosphere.
Source: I spent many days trying to get real answers about eye damage before the eclipse, because "don't look at the sun. Ever." is simply an illogical statement when you consider that all land creatures occasionally glance at the sun accidentally. I can dig up specific, more credible sources if needed - but many of those sources will be generalized statements from eye doctors (at least for the first 3 kinds of damage) - medical studies almost always focus on very, very specific things, whereas these types of eye damage are much broader and beyond the scope of any single study. The closest study to "does looking at the sun for a long time cause eye damage?" was a report accumulating eye damage data from the prior eclipse, where patients went to the doctor after they got vision damage because they stared at it for too long (thus, a very self-selected group, and no one knows how many people watched it without eye damage or without going to the doctor)