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UV radiation damages DNA through two separate mechanisms. Direct damage occurs when a photon is absorbed by DNA. Indirect damage occurs when a photon is absorbed by a chromophore, and the excited chromophore then reacts with DNA, or reacts with other molecules, forming free radicals and causing harm via an oxydative stress mechanism. How far can these free radicals travel? The Wikipedia article on indirect DNA damage states

Unlike direct DNA damage, which occurs in areas directly exposed to UV-B light, free radicals can travel through the body and affect other areas—possibly even inner organs. The traveling nature of the indirect DNA damage can be seen in the fact that the malignant melanoma can occur in places that are not directly illuminated by the sun.

This seems extremely dubious to me, but I know very little about the topic and can't find any more reputable sources discussing the question. Can indirect damage occur in adjacent non-illuminated cells? Can it occur millimeters away from the illuminated area? Centimeters? Can UV light harm inner organs?

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    $\begingroup$ The part about melanoma vs basal cell carcinoma is nonsensical. All types of skin cancer can occur in any area of the skin since things other than UV radiation can damage DNA. $\endgroup$
    – user1850479
    Commented Apr 7, 2020 at 3:02

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The life of the radicals decides how far they move.

This paper https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4310837/#!po=6.92308 has a table of half lives of radicals, the longest lasting ones (the radical of nitrous oxide and nitrogen dioxide) have half lives of seconds.

Diffusion theough the skin would be slow

Technically the problem is "reactive oxygen species" (ROS) and "reactive nitrogen species" (RNS) that are the damaging chemicals that includes free radicals. The reactive species that are not radicals have a longer half-life or are even fairly stable and so could diffuse further before making mischief.

The wikipedia article has problems - that is mentioned on the talk page.

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