When was the first photo of the loch ness monster taken?

The iconic picture you would be referring to is called the "surgeon's photograph". It was taken by Dr Robert Kenneth Wilson (a gynaecologist from London) in 1934. The photo is called the surgeon's photograph as Dr Wilson did not want his name associated with the pictures.

Over many years, there was much speculation of what the object in the picture could be other than the Loch Ness Monster. In 1996 the photo was proved to be a hoax. Marmaduke Wetherell had been ridiculed by an article in the "Daily Mail" newspaper. To get revenge, he took a toy submarine built by his son-in-law, and with the help of some friends, staged the photograph. One of Wetherell's friends then asked Dr Wilson to offer the photograph to the Daily Mail newspaper.