A ray of light passes through four transparent media with refractive indices μ₁, μ₂, μ₃ and μ₄ as shown in Fig. The surfaces of all media are parallel. If the emergent ray CD is parallel to the incident ray AB, we must have

From Snell's law,  we have 

$$\begin{gathered} {\mathrm{\mu }}_1 \sin \mathrm{i} ={\mathrm{\mu }}_2 \sin {\mathrm{r}}_1 \\ {\mathrm{\mu }}_2 \sin {\mathrm{r}}_1 ={\mathrm{\mu }}_2 \sin {\mathrm{r}}_2 \\ {\mathrm{\mu }}_3 \sin {\mathrm{r}}_2={\mathrm{\mu }}_4 \sin \mathrm{e} \\ \mathrm{From} \mathrm{these} \mathrm{equations}, \mathrm{it} \mathrm{follows} \mathrm{that} \\ {\mathrm{\mu }}_1 \sin \mathrm{i} = {\mathrm{\mu }}_4 \sin \mathrm{e} \left(1\right) \\ \mathrm{Ray} \mathrm{CD} \mathrm{will} \mathrm{be} \mathrm{parallel} \mathrm{to} \mathrm{ray} \mathrm{AB}, \mathrm{if} \mathrm{e} = \mathrm{i}. \\ \mathrm{Hence}, {\mathrm{\mu }}_1 = {\mathrm{\mu }}_4. \end{gathered}$$