Straight Lines
Grade None
Question:
<p>A ray of light along x + <span class="math-tex">\(\sqrt 3\)</span>y = <span class="math-tex">\(\sqrt 3\)</span> gets reflected upon reaching x-axis, the equation of the reflected ray is:</p>
<p style="display:inline">y = x + <span class="math-tex">\(\sqrt 3\)</span></p>
<p style="display:inline">y = <span class="math-tex">\(\sqrt 3\)</span>x - <span class="math-tex">\(\sqrt 3\)</span></p>
<p style="display:inline"><span class="math-tex">\(\sqrt 3\)</span>y = x - <span class="math-tex">\(\sqrt 3\)</span></p>
<p style="display:inline"><span class="math-tex">\(\sqrt 3\)</span>y = x - 1</p>
Step-by-Step Solution
Key Concept: The reflected ray's equation is determined by the point of incidence on the x-axis and the mirror image of any point from the incident ray across that axis.
<html><body><p>Suppose B(0, 1) be any point on a given line and the coordinate of A is (<span class="math-tex">$\sqrt 3$</span>, 0). So, the equation of<br/>
<img alt="" data-imgur-src="B8TM3A6.png" src="https://media-mycbseguide.s3.amazonaws.com/images/imgur/1621087848-48yrq8.jpg" style="width: 150px; height: 170px;"/><br/>
Reflected ray is <span class="math-tex">$\frac{-1-0}{0-\sqrt{3}}=\frac{y-0}{x-\sqrt{3}}$</span><br/>
<span class="math-tex">$\Rightarrow$</span> <span class="math-tex">$\sqrt{3} y$</span> = x - <span class="math-tex">$\sqrt{3} $</span></p></body></html>
Correct Answer: C