If hat{i} denotes a unit vector along the inc | vedclass

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(C) Snell's law in vector form relates the incident ray vector $\hat{i}$,the refracted ray vector $\hat{r}$,and the normal vector $\hat{n}$ to the int

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

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(C) Snell's law in vector form relates the incident ray vector $\hat{i}$,the refracted ray vector $\hat{r}$,and the normal vector $\hat{n}$ to the interface.According to the law of refraction,$\mu_1 \sin 	heta_1 = \mu_2 \sin 	heta_2$.In vector notation,where $\hat{n}$ is the normal directed towards the incident medium,the cross product $\hat{i} 	imes \hat{n}$ has a magnitude of $\sin 	heta_1$ (since $\hat{i}$ and $\hat{n}$ are unit vectors).Similarly,$\hat{r} 	imes \hat{n}$ has a magnitude of $\sin 	heta_2$.Thus,the vector form of Snell's law is expressed as $\hat{i} 	imes \hat{n} = \mu (\hat{r} 	imes \hat{n})$,where $\mu$ is the refractive index of the second medium relative to the first.

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

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