Batman is correct and Superman should be glad of it. Of course, the exposure of a superhero's identity is probably not a big deal so as long as he leads a quiet normal life. A Justice League episode in which Lex Luthor took over Flash's body shows us a more likely scenario.
This reminds me of Mike Jacobsen's excellent "Where's Clark?" T-shirt from the NeatoShop.
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Frank Quitely made a great explanation out of this. It's a fantastic study on how Superman changes his posture, facial expresion and a whole lot more than just the glasses.
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