The \( x-y \) plane is the boundary between two transparent media. Medium-1 with \( z \geq 0 \) ...

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The \( x-y \) plane is the boundary between two transparent media. Medium-1 with \( z \geq 0 \) has a refractive index \( \sqrt{2} \) and medium-2 with \( z \leq 0 \) has a refractive index \( \sqrt{3} \). A ray of light in medium-1 given by vector \( \mathbf{A}=6 \sqrt{3} \hat{\mathbf{i}}+8 \sqrt{3} \hat{\mathbf{j}}-10 \hat{\mathbf{k}} \) is incident on the plane of separation. Find the unit vector in the direction of the refracted ray in medium- 2 .
 
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