Question

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. $y-x=0$
• B. $y+x=0$
• C. $2y+x=0$
• D. $y+2x=0$

Answer 1

The correct option is B $y+x=0$

Given:
Equation of linear object, $y=x$
On comparing with the equation of line, $y=mx+c$, we get, slope of line, $m=1$
$\Rightarrow \tan \theta =1$
$\Rightarrow \theta ={45}^{\circ }$ 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.
$\Rightarrow {\theta }^{{}^{\prime }}=-{45}^{\circ }$


From the diagram, it is clear that the equation for the image is a straight line passing through the origin and the slope is, $m^{{}^{\prime }}=\tan (-{45}^{\circ })=-1$
$y=m^{{}^{\prime }}x+c=-x+0$
$\Rightarrow y+x=0$