Can a fire have a shadow
Fire can have a shadow not because the incoming light beam scatters off the light in the flame. On the fundamental level, one beam of light cannot directly interact with another beam of light. … Fires can have shadows because they contain hot air and soot, and not because they contain light.
A shadow is formed any time part of a light beam is blocked or redirected. The shadow region is the region in the light beam where there is less light than in the rest of the beam. This dimmer region tends to take on the shape of the object that is blocking or redirecting some of the light, so we tend to think of a shadow as something that is cast or created by the intercepting object. With this concept in mind, in order for a fire to have a shadow, the fire needs to somehow block or redirect part of another beam of light.
A traditional flame can block or redirect light just fine for the simple reason that a traditional flame is more than just a pillar of light. A traditional hydrocarbon flame contains several components: hydrocarbon fuel molecules and oxygen molecules that are in the process of burning, little solid bits of half-burnt fuel and impurities (called soot or smoke), carbon dioxide and water vapor produced by the burning, light, and hot air. The light that you see in the flame is mostly created by the solid bits of airborne soot heating up so much that they glow via regular incandescence. The interface between the hot air in the flame and the colder surrounding air tends to bend light away from its forward-propagating direction. This deflection of light at the interface of different materials is called refraction. It is the same effect that enables a lens to focus light. Therefore, for the simple reason that a flame contains hot air, it is able to deflect away some of the light in a light beam and cast its own shadow. Hot air tends to rise turbulently. For this reason, shadows created by hot air tend to look like a bunch of dancing ripples. Also, the soot in a flame can absorb light and can therefore also contribute to the creation of a shadow of the flame.
To actually notice the shadow of a fire, the light beam that is going past the fire (e.g. sunlight) must be about as bright or brighter than the light created by the fire itself. Otherwise, the light created by the fire, which spreads out in all directions, will overpower and fill in any dim region created in the other beam of light. For example, pointing a weak flashlight at a roaring campfire will not enable you to see the shadow of the fire. Also, the smaller and cooler a flame is, and the less soot it has, the less it absorbs and redirects light, and therefore the dimmer its shadow will be. Depending on your particular setup, you may or may not be able to see the shadow of a flame with your naked eyes. For best results, you should use a bright light beam, such as direct sunlight, and a fire with lots of heat and soot.
Note that fire can have a shadow not because the incoming light beam scatters off the light in the flame. On the fundamental level, one beam of light cannot directly interact with another beam of light. Light beams never directly bounce off each other, absorb each other, or deflect each other. This is because light consists of quantum particles called photons which are by nature bosons. All bosons are able to overlap with each other, pass through each other, and occupy the exact same state at the exact same location. This is also because photons carry neither electric charge nor magnetic moment. Electromagnetic fields, such as those which constitute light, can only interact with objects that carry electric charge or a magnetic moment. Without any charge or magnetic moment to interact with, one bit of light cannot directly influence in any way another bit of light. Note that one light beam can indirectly deflect another light beam by changing the material that both beams are traveling through, or through more exotic effects, but such effects are not present in traditional flames. Fires can have shadows because they contain hot air and soot, and not because they contain light.