Question

A ray of light along $straight x space plus square root of 3 straight y end root space equals space square root of 3$ get reflected upon reaching X -axis, the equation of the reflected ray is

$straight y equals space straight x plus square root of 3$
$square root of 3 straight y end root space equals space straight x minus square root of 3$
$straight y space equals space square root of 3 straight x end root minus square root of 3$
$square root of 3 straight y end root space equals space straight x minus 1$

Solution

square root of 3 straight y end root space equals space straight x minus square root of 3

Given equation of line
$straight x plus square root of 3 straight y space equals square root of 3 space end root space space space space space.... space left parenthesis straight i right parenthesis straight y equals space 1 minus fraction numerator straight x over denominator square root of 3 end fraction$
Slope of incident ray is $space minus fraction numerator 1 over denominator square root of 3 end fraction$
So, slope of reflected ray must be $fraction numerator 1 over denominator square root of 3 end fraction$ and the point of incident $left parenthesis square root of 3 comma 0 right parenthesis$
So equation of reflected ray
$straight y minus 0 space equals space fraction numerator 1 over denominator square root of 3 end fraction space left parenthesis straight x minus square root of 3 right parenthesis rightwards double arrow space square root of 3 straight y end root space equals space straight x minus square root of 3$

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