Light is a pretty simple beast. In lieu of any interference, it will go on, and on, and on, as we see it doing in the vast, often empty, realms of interstellar and intergalactic space.
Space is a rather unique case, because in between massive objects, light is traveling through something very close to a pure vacuum. This vacuum environment it's traveling through means that there’s very little chance for the light to run into any kind of interference - it's relatively easy for the light to travel enormous distances without anything changing its path or blocking its way.
So what are the options if there is something in the way? Well, light functionally has two options: reflection or absorption. Reflection we’re quite familiar with, as it’s the physics behind seeing yourself in a mirror. This can happen anytime light hits a surface which is smooth, to its perspective. (The smoothness required depends on the wavelength of the light - optical light needs a smoother surface to reflect cleanly off of than radio waves do, which are much longer in wavelength.)
The other option is absorption. This is the process which makes rocks warm in the sun. The rocks are absorbing sunlight over time, and over that time, the energy collected into the rock will warm the surface. Any light can be absorbed, not just the infrared (heat) portion of sunlight. A terrible mirror could absorb enough light that your reflection is only a faint ghost of an image. Unless you’ve got an old filament bulb left in your lamps, you won’t notice an appreciable warming to any of your possessions, because most light bulbs nowadays are designed very specifically not to produce much heat. We can’t see it, and it’s a waste of energy to produce heat which doesn’t help us see the room.
These two options, absorption and reflection, work in tandem with each other, and most materials will do a little of both. Even your standard bathroom mirror absorbs a little of the light that hits it (typically about 10%), and few naturally occurring materials on Earth are perfect light absorbers. Some ultra-black materials are getting very close, but the only truly perfectly absorbing objects around so far are black body objects; an object heated until it glows. (An old filament light bulb would count.)
So, when considering what happens to the light from your light bulb when you switch it off, let’s consider what’s happening when we have the light on. Light is being continually produced by the bulb, which is streaming outwards through the air, mostly unperturbed by having to go through air instead of a vacuum. It will then hit every surface which faces the bulb, and some fraction of it will reflect in the direction of your eyeballs, which will absorb the light, and tell you how bright the room is, along with some information about the objects within the room.
The difference between this situation and switching the light off is simply that you’re no longer replacing the absorbed photons of light with new ones. The last rays of light that the light bulb produced will behave exactly as the rest of the light did: either absorbing into or reflecting off of the various surfaces in your room. The reflected light will bounce until it’s absorbed, but considering how fast the photon can traverse the room, and how few bounces it takes to absorb light, this loss of light is functionally instantaneous.
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