Is it ethical to charge for a wrong diagnosis?

Is it ethical to charge for a wrong diagnosis? I was recently
diagnosed with Fuchs'. I understand that it is a fairly easy disease
to diagnose, but the first two doctors who examined me did not find
it. The first thought my problem was cataracts but was not sure and
he refereed me to a cataract surgeon. The second was an
Ophthalmologist who said my only problem was wrong eyeglass
prescription which was off by .25 diopter in one eye. The cataract
surgeon said Fuchs' and I think he is correct.

Doctor 2 collected most of his fee from Medicare but is now billing me
for refractive prescription. My opinion is if he had made a proper
diagnosis he would not have recommended new glasses to try curing
Fuchs'. Is it ethical for him to bill me in spite of his mistake?
.