Question

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

• A. ${}_3{m}^1$
• B. ${}_3{m}^2$
• C. $\frac{1}{{}_1{m}^4}$
• D. ${}_4{m}^2$

Answer 1

The correct option is C $\frac{1}{{}_1{m}^4}$

$i^{m^j}=\frac{m^i}{m^j}$ where $m^i$ means refractive index of medium $i$ with respect to air

$2^{m^1}\times 3^{m^2}\times 4^{m^3}=\left(\frac{m^2}{m^1}\right)\times \left(\frac{m^3}{m^2}\right)\times \left(\frac{m^4}{m^3}\right)=\frac{m^4}{m^1}=4^{m^1}=\frac{1}{1^{m^4}}$

Hence option (c) is correct answer.