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I always assumed we really want to be careful with cheap sunglasses that don't have UV protection. If the darkening causes the eye to open I assume more UV would be let in so would be better without them. Recently I bought a pair of these as sacrificial boat/sup/beach sunglasses FUMKEN Polarized Sports Sunglasses for Men Women Driving Cycling Climbing Anti-glare UV400 Protection TR90 Unbreakable Frame (Black Frame / Gray Lens) : Amazon.co.uk: Clothing I have a UV torch and tried to light up a £20 note through them. No UV seems to be getting through though its only one part of the spectrum. They are pretty tough seeming, good side protection, clear image and polarising enough to see through the reflection on water though not quite as much as my more expensive ones, perhaps not a bad thing though as those make some screens totally black unless i tilt my head 45 degrees.Your version of cheap and mine are very different.. I've never spent that amount on a pair of sunglasses , until recently always under £10
I've spent my life working in buildings with no windows, therefore I'm sensitive to light and when sailing have always worn Sunglasses, cheap plastic, (you don't want glass around your eyes on a boat) polariod, wrapround.
Glasses on in about an hour and a half when I leave work.