Question

An object is placed symetrically between the two perpendicular plane mirrors as shown in the figure. The equation of the locus of all the images formed by this arrangement is

[Assume the intersection point of the mirrors as the origin.]

• A. $x+y=a$
• B. $(x-a{)}^2+(y-a{)}^2=a^2$
• C. $(x-a{)}^2+ax-a=0$
• D. $x^2+y^2=2a^2$

Answer 1

The correct option is D $x^2+y^2=2a^2$


Since the mirrors are at right angles ($\theta ={90}^{\circ }$) to each other,

Since $\frac{360}{\theta }=\frac{360}{90}=4$ (even number)

$\therefore$ Number of images =$\frac{360}{\theta }-1=3$

All the images and the object are concyclic. The radius of the circle will be $\text{CO}=\sqrt{2}a$ and the centre lies at origin ${}^{\prime }{\text{O}}^{\prime }$.

Equation for the locus (circle) is given by,

${(x-0)}^2+{(y-0)}^2=2a^2$

$\Rightarrow x^2+y^2=2a^2$