Interference from Thin Films — Question 8

Question 8

Changing the incident medium can reverse a film interference condition

A film has $n_f=1.40$ and lies on a substrate with $n_s=1.20$. Initially its incident medium is air, $n_0=1.00$. It is illuminated normally at $\lambda_0=560\,\mathrm{nm}$ and has thickness $t=100\,\mathrm{nm}$. The incident medium is then replaced by a transparent liquid with index 1.60; the film and substrate are unchanged.

1. Classify the reflected phase condition before the liquid is added.

2. Repeat the phase analysis afterward and state whether the new minimum must have zero reflectance.

Question 8 - Solution

Changing the incident medium can reverse a film interference condition

(a) Method and calculation

$$2n_ft=280\,\mathrm{nm}=\lambda_0/2,\quad\Delta\phi_{\mathrm{prop}}=\pi.$$$$1.00<1.40>1.20:\quad\Delta\phi_r=\pi\Longrightarrow\boxed{\delta=2\pi:\ \text{constructive}}.$$

(b) Interpretation and further calculation

$$1.60>1.40>1.20:\quad\Delta\phi_r=0\Longrightarrow\boxed{\delta=\pi:\ \text{destructive}}.$$$$I_{\min}\propto|E_1-E_2|^2\Longrightarrow\boxed{\text{a phase minimum need not be zero}}.$$

Physical check

The normal-incidence propagation phase inside the unchanged film is the same. The top-interface reflection sign is what changes.