In order to protect your eyes in the tanning, you'd better wear the sunglasses with uv rays protection. Thus, your eyes will be protected to some degree. If you just close your eyes in a tanning bed, your eyes will be damaged through the eyes surface skin. It is so bad. You should not do this. You need to find the sunglasses with good role to wear in a tanning bed.
Just closing eyes in a tanning bed is far less than enough to protect your eyes. Tanning bed first became popular in 1970s, because it provided a simple way to get an even golden glow skin color without staying under sunrays day after day. You can control the color by adjust the artificial source. It seemed so convenient and safe that many salons purchased this device and promoted it. But actually it is very dangerous to the skin and eyes. The beds emits ultraviolet radiation to tan your skin, which is a proven carcinogens. The UVR might damages your skin and your eyes at the same time as it tans your skin. The UVR exposure to eyes is as strong as 100 times of the UVR from the sun. How terrible this figure could be! Lying in this kind of bed, closing eyes or wearing sunglasses are just not enough. It is imperative to wear the special goggles to withstand the UV of tanning bed. If your eyes are very dry, you can instill some moisturing eye drops before getting into the tanning bed. My suggestion is, if possible, you'd better not to get tanning. If you insist on tanning, then it is a must for you to wear the special designed goggles. Don't imaging any other ways, which apparently are not functional. Good luck!
It is true that such tanning equipment would generate some damages to your skin and your eyes, for there would be some rays. And my advice for you is to wear a pair of nice sunglasses so that such rays would be resisted. Also, just try not to tan for much too long, in a word, that is not a healthy thing.