|MadSci Network: Anatomy|
Thanks for the question. The answer is, it would depend on several factors-the brightness of the sun on a particular day (influenced by clouds and the height of the sun in the sky), how long you were to stare and of course, if you observed with the naked eye or using a telescope/binoculars.
If you were using the last method, you would be very foolish. A piece of paper held at the eyepiece of a telescope focused on the sun will catch fire almost instantly-as would the front of your eyeball if you were to look into the eyepiece. But as you correctly say, looking at the sun with the naked eye is also very dangerous. The sun emits both infrared (heat) and ultraviolet radiation, both of which would be focused and concentrated onto your retina if you were to stare at the sun. In bright sunlight, the cells at that point on your retina could be damaged beyond repair in a few seconds. In addition, your retina contains a region of very sensitive cells called the yellow spot or fovea. This is responsible for the ability to detect fine details at low light levels and destruction of these cells causes substantial visual impairment.
So, the brief answer to your question is "anywhere from almost instantly to a very few seconds". And remember also there are no pain receptors in the retina, so you wouldn't even know it had happened. I'm sure you know already, but we really can't stress enough the importance of not looking directly at the sun for any length of time, ever, ever, ever. It's incredibly dangerous.
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