To understand how an LCD projector works, it's best to start at the beginning -- with a beam of light -- and end on the movie screen itself.
Step one: A powerful light source emits a beam of intense, white light.
Step two: Our beam of white light bounces off a group of mirrors that includes two dichroic mirrors, which are coated in a special film that reflects only a specified wavelength of light. You know how a prism (or a droplet of water) breaks a beam of light into distinct wavelengths (or a rainbow of colors)? The same principle applies here, only each dichroic mirror breaks off a single specified wavelength. So the white light hits the mirrors, and each reflects a beam of colored light on through the projector: one red, one green and one blue.
Step three: The beams of red, green and blue light each pass through a liquid crystal display composed of thousands of tiny pixels. You can read How Liquid Crystal Displays Work for a more detailed explanation of LCD technology, but it comes down to tiny, colorless pixels that either block light or allow it to pass through when triggered by an electric current. All three of the LCD screens in the projector display the same image or moving images, only in gray scale. When the colored light passes through these three screens, they relay three versions of the same scene: one tinted red, one tinted green and one tinted blue.
Step four: But of course the final image we see isn't red, green or blue; it's full color. So inside the LCD projector, the three tinted versions of this scene recombine in a dichroic prism (a finely crafted combination of four triangular prisms) to form a single image composed of not three colors but millions of colors.
Step five: The light of this vibrant, colorful version of the scene then passes through a projector lens and onto the big screen.
That's really all there is to it. But what are the pros and cons of this technology?