Interference from Thin Films — Question 5

Question 5

Adjacent spectral maxima determine thickness without guessing an order

A nondispersive film of index 1.40 in air is observed in normal reflection. Adjacent reflected maxima occur at vacuum wavelengths $700\,\mathrm{nm}$ and $500\,\mathrm{nm}$, with no maximum between them. There is one relative reflection phase reversal.

1. Use the adjacent-order condition to determine $D=2nt$ and the film thickness.

2. Identify the integer order m in $D=(m+1/2)\lambda_0$ for each wavelength and verify adjacency.

Question 5 - Solution

Adjacent spectral maxima determine thickness without guessing an order

(a) Method and calculation

$$D/\lambda_{500}-D/\lambda_{700}=1\Longrightarrow D=\frac{\lambda_{500}\lambda_{700}}{\lambda_{700}-\lambda_{500}}.$$$$\boxed{D=1750\,\mathrm{nm},\quad t=D/(2n)=625\,\mathrm{nm}}.$$

(b) Interpretation and further calculation

$$1750/700=2.5\Longrightarrow\boxed{m_{700}=2}.$$$$1750/500=3.5\Longrightarrow\boxed{m_{500}=3,\quad m_{500}-m_{700}=1}.$$

Physical check

It is the reciprocal wavelength that advances uniformly with interference order when the index is nondispersive.