If you think Einstein-with-his-tongue-out is the last word in whimsical physicist photography, have a look at this 1931 shot of the Mighty Hip Einie with an Einstein marionette.
Here's the runner up: Einstein in fuzzy slippers.
Dan Bessie writes, "As it happens, I own the original negative (and photo) of Einstein with the marionette, created by my uncle Harry Burnett. And contrary to comments you've received, the puppet is neither Mark Twain, nor was it Photoshopped."
Attributed to Harry Burnett while Yale Puppeteers were working in their theater, Teatro Torito, on Olvera Street in Los Angeles, California, circa 1931. The photo was taken by Harry Burnett at Cal Tech in Pasadena where Albert Einstein was teaching. Einstein saw the puppet perform at the Teato Torito and was quite amused. He reached into his jacket's breast pocket, pulled out a letter and crumpled it up. Speaking in German, he said, "The puppet wasn't fat enough!" He laughed and stuffed the crumpled letter up under the smock to give the puppet a fatter belly. This is a wonderful photograph that Harry treasured. Harry Burnett also kept the letter in a frame and loved to retell the story and at the end give his pixish laugh.