Question 56: Ray Optics

Question

A ray of light travelling in the direction $${1 \over 2}\left( {\widehat i + \sqrt 3 \widehat j} \right)$$ is incident on a plane mirror. After reflection, it travels along the direction $${1 \over 2}\left( {\widehat i - \sqrt 3 \widehat j} \right)$$. The angle of incidence is

Accepted Answer

Let $${\widehat v_i} = {1 \over 2}\left( {\widehat i + \sqrt 3 \widehat j} ight)$$ and $${\widehat v_r} = {1 \over 2}\left( {\widehat i - \sqrt 3 \widehat j} ight)$$ be the unit vectors along the incident and the reflected rays. From Snell's law, angle of incidence (say $$	heta$$) is equal to the angle of reflection. Thus, angle between $$ - {\widehat v_i}$$ and $${\widehat v_r}$$ is 2$$	heta$$.
Using, dot products of vectors, we get
$$\cos (2	heta ) =  - {\widehat v_i}\,.\,{\widehat v_r} = 1/2$$.
Hence, $$	heta  = 30^\circ $$.

Answer

30$$^\circ$$

Answer

45$$^\circ$$

Answer

60$$^\circ$$

Answer

75$$^\circ$$

Ray Optics

A ray of light travelling in the direction ${1 \over 2}\left( {\widehat i + \sqrt 3 \widehat j} \right) is incident on a plane mirror. After reflection, it travels along the direction {1 \over 2}\left( {\widehat i - \sqrt 3 \widehat j} \right)$. The angle of incidence is

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