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JEE Main 20137 April
Exam
JEE Main
Year
2013
Date
7 April
Subject
Mathematics
Chapter
Straight Lines

JEE Main 2013 · 7 April · Mathematics · Straight Lines

A ray of light along x + 3 y = 3 gets reflected upon reaching X -...

A ray of light along x+3y=3x + \sqrt{3}y = \sqrt{3} gets reflected upon reaching X−X -axis, the equation of the reflected ray isA ray of light along x + 3 y = 3 gets reflected upon reaching X - axis, the equation of the reflected ray is

Options

  1. Ay=3x−3y = \sqrt{3}x - \sqrt{3}
  2. B3y=x−1\sqrt{3}y = x - 1
  3. Cy=x+3y = x + \sqrt{3}
  4. D3y=x−3\sqrt{3}y = x - \sqrt{3}

Correct answer

D. 3y=x−3\sqrt{3}y = x - \sqrt{3}

Step-by-step solution

Let incident ray intersecting Y−Y -axis at BB and X−X -axis at AA.

A ray of light along x + 3 y = 3 gets reflected upon reaching X - axis, the equation of the reflected ray is

∆OAB∆ OAB is congruent to ∆OAB′∆ OA{B}^{'}

Hence OB′=OBO{B}^{'} = OB

Equation of B′A:x3+y−1=1{B}^{'}A: \dfrac{x}{\sqrt{3}} + \dfrac{y}{- 1} = 1

or x−3y=3x - \sqrt{3}y = \sqrt{3}.

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