Question

$n_{12}\times n_{21},$ in simplest from is

• A. 1
• B. 2
• C. 0
• D. 4

Answer 1

The correct option is A 1

Suppose ${\eta }_1$ and ${\eta }_2$ is the refractive index of medium $1$ and $2$.

The refractive index of the medium $1$ with respect to the medium $2$ is given as

${\eta }_{12}=\frac{{\eta }_1}{{\eta }_2}$

Similarly the refractive index of the medium $2$ with respect to the medium $1$ is given as

${\eta }_{21}=\frac{{\eta }_2}{{\eta }_1}$

Hence,

${\eta }_{12}\times {\eta }_{21}=\frac{{\eta }_1}{{\eta }_2}\times \frac{{\eta }_2}{{\eta }_1}$

${\eta }_{12}\times {\eta }_{21}=1$.