Question

if $\hat{i},\hat{r},\hat{n}$ are unit vectors along incident ray in air, refracted ray in a medium, normal respectively and $\mu$ is refractive index of medium, then the correct choice is :

• A. ($\hat{i}\times \hat{n})=\mu (\hat{n}\times \hat{r}$)
• B. $\mu (\hat{i}\times \hat{n})=\hat{n}\times \hat{r}$
• C. $\hat{i}.\hat{n}=\mu (\hat{n}.\hat{r}$)
• D. $\mu (\hat{i}.\hat{n})=\hat{n}.\hat{r}$

Answer 1

The correct option is A ($\hat{i}\times \hat{n})=\mu (\hat{n}\times \hat{r}$)

By Snell's Law,
$sini=\mu sinr$

And $\left|\hat{i}\right|=1,\left|\hat{n}\right|=1,\left|\hat{r}\right|=1$

So, we can write equation 1 as $\left|\hat{i}\right|\left|\hat{n}\right|sini=\mu \left|\hat{r}\right|\left|\hat{n}\right|sinr$

where $i$ is the angle between $\hat{i}$ and $\hat{n}$ while $r$ is the angle between $\hat{n}$ and $hatr$.
$⟹(\hat{i}\times \hat{n})=\mu (\hat{n}\times \hat{r})$