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I want to make something like a laser projector for an experiment but with common light.

My question is: is this possible to focus a small point of common light to the wall and control it with mirrors? What combination of lenses I'll need for it?

Thanks!

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"A common light" needs to be defined better. I assume you want to use an incoherent source such as an LED or an incandescent light. The size of the smallest spot to which a light beam can be focused depends on the size of the light source. Imagine, for example, trying to focus light from the Sun to a small spot. In essence, this means forming a small image of the Sun. If you study how a lens works (e.g., this figure from Wikipedia illustrating the geometry of image formation by a lens), you'll see that the angle from the lens to the two sides of the image is the same as the angle from the lens to the two sides of the Sun. lens diagram

A smaller spot can be formed from sunlight only by imaging a smaller portion of the Sun. So, in order to form a small spot from an ordinary incoherent light source, with the spot at a distance from the lens, you would need a source that is extremely bright and extremely small. There really is nothing that easily fits the bill. A diode laser works fine, but is coherent and therefore not "ordinary".

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An alternative to consider is to use a strong light source for example halogen lamp, which is typically used in fiber optic illuminator.

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