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Question

A ray of light traveling along the line x+y=1 is inclined on the x-axis and after refraction, it enters the other side of the x-axis by turning 15° away from the x-axis. The equation of the line along which the refraction ray travels is


A

3y-x+1=0

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B

3y+x+1=0

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C

3y+x-1=0

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D

None of the above

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Solution

The correct option is D

None of the above


Step 1: Given data

Equation of line =x+y=1

The angle of the refracted ray with x-axis=15°

Step 2: Formula used

The slope of the line m=tanθ

The point-slope form =(yy1)=m(xx1)

Step 3: Solution

The diagrammatic representation of the given data is:

As the slope of given line x+y=1 is -1,

Then θ=135°, and in case if it's going straight, then the rest of the angle is 180°-135°=45°

But it bends furthermore 15° about the x-axis, So total angle of inclination is 45°+15°=60°

The slope of the line after bending, m =tan(180°-60°)[Fromgivendiagram]

=tan120°=-3

Slope point form of the line at point (1,0)

=(yy1)=m(xx1)

(y-0)=-3(x-1)(y-0)=-3x+3y+3x=+3

Hence, the correct option is D.


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