Question

A unit vector along the incident ray of light is $\hat{i}$. The unit vector for the corresponding refracted ray of light is $\hat{r}\cdot \hat{n}$, a unit vector normal to the boundary of the medium and directed towards the incident medium. If $\mu$ is the refractive index of the medium, then Snell's law (second law) of refraction is :

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

Answer 1

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

Vector form of snell's law is given as

${\mu }_1(\hat{i}\times \hat{n})=(\hat{r}\times \hat{n}){\mu }_2$

$\hat{i}\times \hat{n}=\mu (\hat{r}\times \hat{n})$