If hati denotes a unit vector along incident light ray, hatr a unit vector along refracted ray into a medium of refractive index μ and hatn unit vector normal to boundary of medium directed towards incident medium, then law of refraction is

Question

If hati denotes a unit vector along incident light ray, hatr a unit vector along refracted ray into a medium of refractive index μ and hatn unit vector normal to boundary of medium directed towards incident medium, then law of refraction is (A)  hati ⋅ hatn=μ( hatr ⋅ hatn) (B)  hati × hatn=μ( hatn × hatr) (C)  hati × hatn=μ( hatr × hatn) (D) μ( hati × hatn)= hatr × hatn

Tardigrade Admin · Accepted Answer

Snell's law in vector form is hati × hatn=μ( hatr × hatn)

Q. If $\hat{i}$ denotes a unit vector along incident light ray, $\overset{r}{^}$ a unit vector along refracted ray into a medium of refractive index $μ$ and $\overset{n}{^}$ unit vector normal to boundary of medium directed towards incident medium, then law of refraction is

$\hat{i} \cdot \overset{n}{^} = μ (\overset{r}{^} \cdot \overset{n}{^})$

$\hat{i} \times \overset{n}{^} = μ (\overset{n}{^} \times \overset{r}{^})$

$\hat{i} \times \overset{n}{^} = μ (\overset{r}{^} \times \overset{n}{^})$

$μ (\hat{i} \times \overset{n}{^}) = \overset{r}{^} \times \overset{n}{^}$

Snell's law in vector form is $\hat{i} \times \overset{n}{^} = μ (\overset{r}{^} \times \overset{n}{^})$

Q. If i^ denotes a unit vector along incident light ray, r^ a unit vector along refracted ray into a medium of refractive index μ and n^ unit vector normal to boundary of medium directed towards incident medium, then law of refraction is

i^⋅n^=μ(r^⋅n^)

i^×n^=μ(n^×r^)

i^×n^=μ(r^×n^)

μ(i^×n^)=r^×n^