A thin film of refractive index $\mu =1.5$ and thickness $t=100\text{ nm}$ is illuminated by white light at normal incidence. Which wavelength $\lambda$ in the visible range $400\text{ nm}$ to $700\text{ nm}$ will be strongly reflected?

Solution

1. For a thin film with refractive index $\mu =1.5$ and thickness $t=100\text{ nm}$, the condition for strong reflection at normal incidence is $2\mu t=(m+0.5)\lambda$.
2. Substituting the given values, we get $2(1.5)(100)=(m+0.5)\lambda$, which simplifies to $300=(m+0.5)\lambda$.
3. Solving for $\lambda$, we find $\lambda =\frac{300}{m+0.5}\text{ nm}$.
4. For $m=0$, we calculate $$\begin{array}{rl}\lambda & =\frac{300}{0.5}\\ & =600\text{ nm}\end{array}$$, which falls within the visible range.
5. Hence the answer is (C).