Question 192: Ray Optics

Question

The incident ray, reflected ray and the outward drawn normal are denoted by the unit vectors $$\overrightarrow a $$, $$\overrightarrow b $$ and $$\overrightarrow c $$ respectively. Then choose the correct relation for these vectors.

Accepted Answer

Here $$\overrightarrow a  = \left| {\overrightarrow a } ight|\sin 	heta \widehat i - \left| {\overrightarrow a } ight|\cos 	heta \widehat j$$
As $$\overrightarrow a $$ is an unit vector, so $$\left| {\overrightarrow a } ight|$$ = 1
$$ 	herefore $$ $$\overrightarrow a  = \left| {\overrightarrow a } ight|\sin 	heta \widehat i - \left| {\overrightarrow a } ight|\cos 	heta \widehat j$$
= $$ \sin 	heta \widehat i - \cos 	heta \widehat j$$
Similarly $$\overrightarrow b  = \sin 	heta \widehat i + \cos 	heta \widehat j$$
and $$\overrightarrow c  = \widehat j$$
From option (B),
$$\overrightarrow a $$ $$-$$ 2 ($$\overrightarrow a $$ . $$\overrightarrow c $$)$$\overrightarrow c $$
= $$\sin 	heta \widehat i + \cos 	heta \widehat j$$ = $$\overrightarrow b $$

Answer

$$\overrightarrow b $$ = $$\overrightarrow a $$ + 2$$\overrightarrow c $$

Answer

$$\overrightarrow b $$ = $$\overrightarrow a $$ $$-$$ 2 ($$\overrightarrow a $$ . $$\overrightarrow c $$)$$\overrightarrow c $$

Answer

$$\overrightarrow b $$ = 2$$\overrightarrow a $$ + $$\overrightarrow c $$

Answer

$$\overrightarrow b $$ = $$\overrightarrow a $$ $$-$$ $$\overrightarrow c $$

Ray Optics

The incident ray, reflected ray and the outward drawn normal are denoted by the unit vectors $\overrightarrow a , \overrightarrow b and \overrightarrow c $ respectively. Then choose the correct relation for these vectors.

Choose the correct answer: