Question

If $\mu ,$ represents the refractive index when a light ray goes from medium i to j, then ${}_2{\mu }_1\text{x}{}_3{\mu }_2\text{x}{}_4{\mu }_3$ is equal to

• A. ${}_3{\mu }_1$
• B. ${}_3{\mu }_2$
• C. $\frac{1}{{}_1{\mu }_4}$
• D. ${}_4{\mu }_2$

Answer 1

The correct option is C $\frac{1}{{}_1{\mu }_4}$

According to the question,

${}_2{\mu }_1{\times }_3{\mu }_2{\times }_4{\mu }_3=\frac{{\mu }_1}{{\mu }_2}\times \frac{{\mu }_2}{{\mu }_3}\times \frac{{\mu }_3}{{\mu }_4}=\frac{{\mu }_1}{{\mu }_4}{=}_4{\mu }_1=\frac{1}{{}_1{\mu }_4}$