If i^ denotes a unit vector along an incident ray, r^ a unit vector along the refracted ray into a medium of refractive index 'μ' and n^ a unit vector normal to the boundary of the media directed towards the incident medium, then the law of refraction can be written as

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If $\hat{i}$ denotes a unit vector along an incident ray, $\hat{r}$ a unit vector along the refracted ray into a medium of refractive index ' $μ$ ' and $\hat{n}$ a unit vector normal to the boundary of the media directed towards the incident medium, then the law of refraction can be written as

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

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

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

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

answer is C.

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Detailed Solution

$\begin{array}{l} \hat{i} \times \hat{n} = 1 \times 1 \times sini, perpendicular to plane of incidence \\ \hat{r} \times \hat{n} = 1 \times 1 \times sinr, perpendicular to plane of incidence in the same direction \\ ∴ \frac{\hat{i} \times \hat{n}}{\hat{r} \times \hat{n}} = \frac{sini}{sinr} = μ \end{array}$