Question:
A ray of light along \(x + \sqrt{3}\,y = \sqrt{3}\) gets reflected upon reaching \(X\)-axis, the equation of the reflected ray is :
A ray of light along \(x + \sqrt{3}\,y = \sqrt{3}\) gets reflected upon reaching \(X\)-axis, the equation of the reflected ray is :
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The incident ray meets the x-axis at a point; the reflected ray passes through the same point with slope of opposite sign.
Updated On: Nov 13, 2026
- \(y = x + \sqrt{3}\)
- \(\sqrt{3}\,y = x - \sqrt{3}\)
- \(y = \sqrt{3}\,x - \sqrt{3}\)
- \(\sqrt{3}\,y = x - 1\)
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The Correct Option is B
Solution and Explanation
Incident line: \(x + \sqrt{3}y = \sqrt{3}\), slope \(= -\frac{1}{\sqrt{3}}\).
It meets the X-axis (put \(y=0\)) at \(P(\sqrt{3}, 0)\).
On reflection from the X-axis the slope changes sign, so the reflected ray has slope \(+\frac{1}{\sqrt{3}}\) and passes through \(P\).
Equation: \(y - 0 = \frac{1}{\sqrt{3}}(x - \sqrt{3})\), i.e. \(\sqrt{3}\,y = x - \sqrt{3}\).
Answer: (2) \(\sqrt{3}\,y = x - \sqrt{3}\)
It meets the X-axis (put \(y=0\)) at \(P(\sqrt{3}, 0)\).
On reflection from the X-axis the slope changes sign, so the reflected ray has slope \(+\frac{1}{\sqrt{3}}\) and passes through \(P\).
Equation: \(y - 0 = \frac{1}{\sqrt{3}}(x - \sqrt{3})\), i.e. \(\sqrt{3}\,y = x - \sqrt{3}\).
Answer: (2) \(\sqrt{3}\,y = x - \sqrt{3}\)
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