Question

Two plane mirror are inclined as shown in figure an object is placed at origin. 1st reflection takes place from $M_1$ and then from $M_2$. Calculate the coordinates of final image.

Answer 1

$OC=d\sin {45}^o=\frac{d}{\sqrt{2}}$

Object distance for lower mirror is $OC$

$O{I}_1=2OC=\sqrt{2}d$

$A{I}_1=O{I}_1\sin {45}^o=2d$

Object distance for upper mirror is $B{I}_1$

$B{I}_1=AB+A{I}_1=3d$

Image distance is hence, $B{I}_2=B{I}_1=3d$

$A{I}_2=B{I}_2+AB=4d$

Hence, coordinates of final image is $(OA,I_{2}A)=(d,4d)$