There is a popular belief that wet skin burns or tans faster. However, I've never heard a believable explanation of why this happens.
The best explanation I've heard is that the water droplets on the skin act as a lens, focusing the sunlight onto your skin. I don't see how this would affect an overall burn, because the amount of sunlight reaching the skin is the same (ignoring reflection).
Is this 'fact' true, and if so, what causes it?
Answer
I don't know of any research to find out if skin sunburns faster when wet, though someone did a comparable experiment to find out if plants can be burnt by sunlight focussed through drops of water after the plants have been watered.
You need to be clear what is being measured here. The total amount of sunlight hitting you, and a plant, is unaffected by whether you're wet or not. The question is whether water droplets can focus the sunlight onto intense patches causing small local burns.
The answer is that under most circumstances water droplets do not cause burning because unless the contact angle is very high they do not focus the sunlight onto the skin. Burning (of the plants) could happen if the droplets were held above the leaf surface by hairs, or when the water droplets were replaced by glass spheres (with an effective contact angle of 180º).
My observation of water droplets on my own skin is that the contact angles are less than 90º, so from the plant experiments these droplets would not cause local burning. The answer to your question is (probably) that wet skin does not burn faster. I would agree with Will that the cooling effect of water on the skin may make you unaware that you're being burnt, and this may lead to the common belief that wet skin accelerates burning.
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