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Q.

A ray of light travelling along the line x + 3y = 5 is incident on the x-axis and after refraction it enters the other side of the x-axis by turning $\frac{π}{6}$ away from the x-axis. The equation of the line along which the refracted ray travels is

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a

$\sqrt{3} x + y - 5 \sqrt{3} = 0$

b

$\sqrt{3} x - y - 5 \sqrt{3} = 0$

c

$x - \sqrt{3} y - 5 \sqrt{3} = 0$

d

$x + \sqrt{3} y - 5 \sqrt{3} = 0$

answer is C.

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Detailed Solution

The refracted ray passes through the point (5, 0) and makes an angle 120º with positive direction of x-axis

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$∴$ The equation of the refracted ray is (y – 0) = tan 120º (x – 5)

$\Rightarrow y = - \sqrt{3} (x - 5) o r \sqrt{3} x + y - 5 \sqrt{3} = 0$

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A ray of light travelling along the line x + 3y = 5 is incident on the x-axis and after refraction it enters the other side of the x-axis by turning π6away from the x-axis. The equation of the line along which the refracted ray travels is