question_answer

A ray of light along\[x+\sqrt{3}y=\sqrt{3}\]gets reflected upon reaching x−axis, the equation of the reflected ray is:     AIEEE Solevd Paper-2013

A) \[y=x+\sqrt{3}\]                              

B) \[\sqrt{3y}=x-\sqrt{3}\]               

C) \[y=\sqrt{3}x-\sqrt{3}\]               

D) \[\sqrt{3}y=x-1\]

Correct Answer: B

Solution :

Slope of \[x+\sqrt{3}y=\sqrt{3}\]is \[-\frac{1}{\sqrt{3}}={{m}_{1}}\](let) So, \[tan\text{ }\theta =-\frac{1}{\sqrt{3}}\] \[\theta =150{}^\circ \] So, slope of reflected ray is \[tan\text{ }30{}^\circ =\frac{1}{\sqrt{3}}\] So, equation of reflected ray is \[y-0=\frac{1}{\sqrt{3}}\text{(}x-\sqrt{3})\] \[\sqrt{3}y=x-\sqrt{3}\]