Question

An object is kept in front of three mutually perpendicular mirrors. Then the total number of images is.

Answer 1

The three mutually perpendicular mirrors form an image in every quadrant of the $3$ dimensional space with an intersecting point of the $3$ mirrors as the centre of the space.
So let's demonstrate this by denoting anything that is in a quadrant space of $3$-dimensional space by $xyz{x}^{\prime }{y}^{\prime }{z}^{\prime }$, where $x,y,z$ are positive axes and $x^{\prime },y^{\prime },z^{\prime }$ are negative axes. so in this way, our given object is in $xyz$ space($xyz$ quadrant where all $x,y,z$ are positive).
Now the 3 planes of the $xyz$ quadrant,i.e $xy$ plane, $yz$ plane,and $zx$ plane are mirrors and so they form corresponding mirror images in $xy{z}^{\prime },yz{x}^{\prime }$ , and $zx{y}^{\prime }$ quadrants. and also considering the mirror images of the $3$ images formed directly from the object, we get an image in every quadrant of the $3$-dimensional space except the quadrant containing the object itself,
So the total images formed are $7.$