Question

If ${}_i{\mu }^j$ represents refractive index when a light ray goes from medium i to medium j. Then the product ${}_2{\mu }^1{\times }_3{\mu }^2{\times }_4{\mu }^3$ is equals to

• A. ${}_3{\mu }^1$
• B. ${}_3{\mu }^2$
• C. ${}_4{\mu }^1$
• D. ${}_4{\mu }^2$

Answer 1

Answer: (C)

${}_4{\mu }^1$

Given: ${}_i{\mu }_j=\frac{{\mu }_i}{{\mu }_j}$
So, ${}_2{\mu }^1{\times }_3{\mu }^2{\times }_4{\mu }^3=\frac{{\mu }_2}{{\mu }_1}\times \frac{{\mu }_3}{{\mu }_2}\times \frac{{\mu }_4}{{\mu }_3}$
$=\frac{{\mu }_4}{{\mu }_1}$
${=}_4{\mu }^1$