Question

A ray of light travelling along the line $x+y=1$ is incident on the X-axis and after refraction, it enters the other side of the X-axis by turning ${15}^{\circ }$ away from the x-axis. The equation of the line along which the refracted ray travels is

• A. $y+\sqrt{3}x-\sqrt{3}=0$
• B. $(2-\sqrt{3})x+y=1$
• C. $y+(2+\sqrt{3})x=2+\sqrt{3}$
• D. None of these

Answer 1

The correct option is A $y+\sqrt{3}x-\sqrt{3}=0$

The refracted ray passes through the point $(1,0)\equiv (x_1,y_1)$ and makes an angle

$120$ degree with the positive $x-axis$

$(y-y_1)=m(x-x_1)$

$(y-0)=\tan 120(x-1)$

$\Rightarrow y=-\sqrt{3}(x-1)$

$\Rightarrow y=-\sqrt{3}x+\sqrt{3}$

$\Rightarrow y+\sqrt{3}x-\sqrt{3}=0$

slope $=\tan ({180}^o-{60}^o)$

$=\tan \left({120}^o\right)$

$=-\sqrt{3}$