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

The unit vector along incident $$ray2i^$$−$$3j^+4k^29the$$ unit vector along $$NormalN^=3i^$$−$$6j^+2k^7The$$ unit vector along reflected $$rayR^=I^$$−$$2I^$$.$$N^N^solving$$ we $$getR^=$$−$$94i^$$−$$237j^+68k^4929$$

Ray optics

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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 $3 \hat{i} - 6 \hat{j} + 2 \hat{k} .$

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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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Ray optics

Remember concepts with our Masterclasses.

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

The unit vector along incident ray2i^−3j^+4k^29the unit vector along NormalN^=3i^−6j^+2k^7The unit vector along reflected rayR^=I^−2I^.N^N^solving we getR^=−94i^−237j^+68k^4929

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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 $3 \hat{i} - 6 \hat{j} + 2 \hat{k} .$