First slide

Ray optics

Question

A ray of light is incident on a plane mirror, along the direction given by vector $2 \hat{i} - 3 \hat{j} + 4 \hat{k} .$ Find the unit vector along reflected ray. Take normal to mirror along the direction of vector $3 \hat{i} - 6 \hat{j} + 2 \hat{k} .$

Difficult

Solution

$\begin{array}{l} The u nit vector along incident ray \\ \frac{2 \hat{i} - 3 \hat{j} + 4 \hat{k}}{\sqrt{29}} \\ the u nit vector along Normal \\ \hat{N} = \frac{3 \hat{i} - 6 \hat{j} + 2 \hat{k}}{7} \\ The u nit vector along reflected ray \\ \hat{R} = \hat{I} - 2 (\hat{I} . \hat{N}) \hat{N} \\ solving we get \\ \hat{R} = \frac{- 94 \hat{i} - 237 \hat{j} + 68 \hat{k}}{49 \sqrt{29}} \end{array}$

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