Straight Lines
Reflection and Image Formation
Grade 11
Question:
<p>A ray of light coming from the point <i>(2, 2√3)</i> is incident at an angle 30° on the line <i>x = 1</i> at the point A. The ray gets reflected on the line <i>x = 1</i> and meets X-axis at the point B. Then, the line AB passes through the point</p>
<p>(a) <i>(1/4, -3)</i></p>
<p>(b) <i>(3, -√3/2)</i></p>
<p>(c) <i>(3, -3)</i></p>
<p>(d) <i>(4, -3)</i></p>
Step-by-Step Solution
Key Concept: Use the law of reflection: the incident and reflected rays make equal angles with the normal to the reflecting surface. Find the reflected ray equation and determine which option lies on it.
<p><strong>Step 1:</strong> The line <i>x = 1</i> is equidistant from point <i>P(2, 2√3)</i> and the Y-axis. So, <i>P'(0, 2√3)</i> and according to the concept of reflection, the line passes through <i>P'(0, 2√3)</i>.</p><p><strong>Step 2:</strong> As the angle <i>∠P'BX = ∠ABX = 120°</i>, the slope of line AB is <i>tan 120° = -√3</i>.</p><p><strong>Step 3:</strong> Equation of line AB is <i>y - 2√3 = -√3(x - 0)</i></p><p><strong>Step 4:</strong> This simplifies to <i>√3x + y = 2√3</i>.</p><p><strong>Step 5:</strong> From the options, the line passes through the point <i>(3, -3)</i>.</p><p>∴ Answer is (c).</p>
Correct Answer: C