Question

A thin layer of liquid methylene iodide (n = 1.756) is sandwiched between two flat, parallel plates of glass (n = 1.50). What must be the thickness of the liquid layer if normally incident light with λ = 581 nm in air is to be strongly reflected?

Answer 1

There is a phase shift of ½λ for rays reflected off the top of the liquid layer (as liquid n > glass)
There is no phase shift with reflection off the bottom of the layer (as glass n < liquid)

Reflected rays off the top will combine constructively when alongside waves having a path difference of ½ wave (or 1½, 2½ ....) caused by travelling through the liquid.

The minimum thickness (t) for a path diff. of ½ wave is given by
2 t = ½ λ' .. (λ' = wavelength in liquid = λair / n)

t = ¼( λ / n) .... ... (0.25)*(581E-9 m) / (1.756)

t = 82.7E-9 m