Observations and results
When you lit one of the tea candles and looked through the CD case from the first side, your eyes detected both the light coming directly from the unlit candle and the reflected light emitted by the lit candle's flame. This reflected light creates a virtual image of the flame appearing behind the transparent panel. We interpret virtual images as appearing behind the reflective surface that creates them because our brains naturally interpret light from visible objects as traveling to our eyes in straight lines. Light from the lit candle is reflected by the "mirror," but our brain's tendency is to "unfold" that light , placing a virtual image of the lit candle behind the transparent plastic (and apparently right on top of the actual location of our unlit candle). Light from the lit candle doesn't actually travel to your eye from behind the transparent plastic (as we know the light is only coming from the candle on the front side of the plastic)—but it looks like it does!
This overlapping can be attributed to a property of light known as superposition, meaning that visible light can represent the combination of many sources simultaneously. The light rays coming from the unlit candle and the reflected light rays of the lit candle are superposed on top of one another. In situations where one source of light is much stronger than another, only the stronger source is clearly visible. This helps explain why things that seem bright in the dark (like stars) don't seem that bright or are invisible when the sun is out.
Every surface exhibits some transmission and some reflection. For very transparent substances like glass, only about 5 percent of the light that hits it is reflected. The remaining 95 percent is transmitted—it passes right on through. When you light one of the tea candles in a dark room, some of its light is transmitted through the CD case, and some of it is reflected. Even though the case can only reflect something like 5 percent of the flame's light, that reflected light is more than enough to create an illusion of two flames as opposed to one flame and one unlit wick.
This same basic manipulation of virtual images has been utilized on stage for decades as a technique known as Pepper's ghost . It's how Disneyland creates The Haunted Mansion's ghouls . It's so compelling that the setup of the illusion has changed very little since its introduction in the mid 19th century!
More to Explore
Candle Illusion, from the University of California, Los Angeles, Department of Physics and Astronomy
Candle Illusion, from YouTube
The Candle illusion: Real and Virtual Images, from Education.com
Make a Mind-Bending Illusion!, from Education.com
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