Question

By an anodizing process, a transparent film of aluminium oxide of thickness $t = 250$ nm and index of refraction $n_2 = 1.80$ is deposited on a sheet of polished aluminium. Which wavelength will be strongly reflected if utensils made from this sheet with observer in white light? Assume normal incidence of the light.

Answer 1

450 nm

Answer 2

The phenomenon is thin-film interference. For normal incidence, the optical path difference (OPD) is $2n_2t$. Reflections at both interfaces (air-oxide and oxide-metal) involve a $\pi$ phase shift. For constructive interference (strong reflection), the condition is $2n_2t = n\lambda$. Given $t=250$ nm and $n_2=1.80$, the OPD is $2 \times 1.80 \times 250 \, \text{nm} = 900 \, \text{nm}$. So, $\lambda = \frac{900}{n}$ nm. For $n=2$, $\lambda = \frac{900}{2} = 450$ nm, which is in the visible range. For $n=1$, $\lambda = 900$ nm (not visible). For $n=3$, $\lambda = 300$ nm (not visible).