Question

If ${}_3{\mu }_1$ 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 equal to:

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

Answer 1

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

If ${}_3{\mu }_1$ represents redfractive index when a light ray goes from medium I to medium j

Then

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

${=}_4{\mu }_1$

$=\frac{1}{{}_1{\mu }^4}$