A plane mirror with reflecting surface facing along +y - axis is placed along +x - axis. The equation of a linear object kept in front of the mirror is y=x as shown in figure. The equation of its image will be
A
y−x=0
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B
y+x=0
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C
2y+x=0
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D
y+2x=0
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Solution
The correct option is By+x=0 Given:
Equation of linear object, y=x
On comparing with the equation of line, y=mx+c, we get, slope of line, m=1 ⇒tanθ=1 ⇒θ=45∘ anticlockwise with +x - axis or mirror.
So, the image will also make the same angle with the plane mirror but in clockwise direction with +x - axis or mirror. ⇒θ′=−45∘
From the diagram, it is clear that the equation for the image is a straight line passing through the origin and the slope is, m′=tan(−45∘)=−1 y=m′x+c=−x+0 ⇒y+x=0