No, light does not take up physical space because it is made up of particles called photons that have no mass and do not occupy physical space.
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No, your mirror reflection does not occupy physical space. It is simply a reflection of light bouncing off the mirror's surface.
Light is not matter because it does not have mass and does not take up physical space like matter does. Light consists of electromagnetic waves that travel at high speeds through space.
A mathematical point in space has no dimensions therefore takes up no space. Certain particles have no rest mass but have the energy equivalent because of the velocity they possess. A singularity is a theoretical no volume point but has a huge mass.
Mass and energy do not take up physical space in the same way that matter does. They are properties of matter that contribute to its overall characteristics, such as its gravitational and kinetic effects, but they do not occupy space in the same sense as solid or liquid objects.
Light can fill a room without taking up physical space.