White light may be considered to be a mixture of wavelengths  with $\lambda$ ranging between $3900\stackrel{0}{A}$ to $7800\stackrel{0}{A}$  . An oil film of thickness $10,000\stackrel{0}{A}$ is examined normally by reflected light. If $\mu =1.4$ , then the film appears bright for

The film appears bright when the path difference $\left(2\mu t\cos r\right)$ is equal to odd multiple of $\lambda /2.$

$$\begin{gathered} i.e., 2\mu t\cos r=\left(2n-1\right)\frac{\lambda }{2} \\ where n = 1,2,3\dots \\ \therefore \lambda = \frac{4\mu t\cos r}{\left(2n-1\right)}=\frac{4\times 1.4\times 10,000\times {10}^{-10}\times \cos 0^0}{\left(2n-1\right)}=\frac{56000}{\left(2n-1\right)}\stackrel{0}{A} \left\{For normal incidence r= 0^o\right\} \\ \Rightarrow \lambda =56000\stackrel{0}{A},18666\stackrel{0}{A},11200\stackrel{0}{A}, 8000\stackrel{0}{A},6222\stackrel{0}{A},5091\stackrel{0}{A},4308\stackrel{0}{A},3733\stackrel{0}{A}. \\ The wavelengths which are not within specified range are to be refracted. \end{gathered}$$