This sounds like a really daft question, but I am trying to clarify details on foundations on thermodynamics to myself, which will involve asking really (seemingly) basic things. When you have two systems with a diathermal (heat and work permitting) boundary between the two systems, we know the t...

Suppose I place two glass slabs with different thickness and refractive indices in a YDSE setup. I was told that if $$ (\mu_1-1)t_1=(\mu_2-1)t_2 $$ then there would be no change in the interference pattern, as compared to the one without any glass slab. Why isn't this true for $$\mu_1 t_1=\mu_2 t...