# thin film interference of light In a thin film interference (reflective system) I know that condition for maxima is $$2\mu t\cos(r)=(2n\pm 1)\frac{\lambda}{2}$$ and for minima is $$2\mu t\cos(r)=n\lambda$$ and for transitive system it's just the opposite. but what happens if then film is very small such that $$\lim_{t \to 0}$$ i.e. thin film is too thin? My teacher told my that condition for minima is satisfied because then $\delta x = \lambda /2$ and hence film appears dark. How is this possible? and similarly what happens of film in too thick ? I am guessing interference does't happen then , but what would be explanation for it ?

At the reflection in an interface from low to high refractive index, a phase shift of $\pi/2$ occurs; no such phase shift occurs on the second interface (high to low). As a consequence, for sufficiently thin films, there is indeed destructive interference- so your very thin film looks dark. You can sometimes see this on soap bubbles just before they pop - the go from shiny and colorful to (patches of) dull and colorless, usually at the top (as liquid is pulled to the bottom of the bubble by gravity).