Pinhole projection is a tiny hole that means all the light rays go from a single point in the scene to a single point in the projected image. That 1 to 1 relationship is how it projects a clear image.
The longer the tube the bigger (and dimmer nothing is free in optics) the projected image (if you made a pinhole projector that had the pinhole on earth and the screen 1 AU away you could project a very dim image of the sun’s surface the same size as the sun).
By shading the screen, we increase the contrast between the relatively bright solar image and the shadows.
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Suppose you want to make an image on a white sheet of paper of a scene. This scene might be a scene of a table with a bowl of fruit on it, or even an image of the sun itself as the moon passes in front of it. They key is that whatever scene you want to project onto the sheet of paper will have light coming from it; that is how you would see the scene directly, and it is that light you want to bounce off the paper into your eyes.
If you just expose the paper to the light coming from the scene… it doesn’t work. Light from the table will be scattered across the entire surface of the paper, as will light from the bowl, and the fruit, etc. It will just be jumbled together and you won’t be able to distinguish any image!
What you need is some way to sort the incoming light so that only light from one particular direction can fall on the paper in one specific spot, and light from all other directions is blocked. The way you can do this is to place a barrier between the paper and the scene into which you put a single, tiny hole. Light travels in straight lines so there is only one path from a particular part of the scene through the hole to reach the paper (subject to the limits of how small your hole can be).
Now you get much less light passing through overall but you can see an image of the scene on your paper. This sorting of light done by the hole is what a focusing lenses do in a camera, except the lenses are designed to sort the light through a larger aperture than the tiny hole. The essence of the task is the same though: Make sure only light incoming from a particular direction makes it a particular part of the imaging sensor or film in the camera.
For imaging a solar eclipse this is very useful because a major problem in observing an eclipse is that the sun is dangerously bright and shouldn’t be looked at directly. The “pinhole camera” naturally greatly restricts the amount of light it allows to pass through and makes the resulting projected image safe to observe. It is also conveniently easy to make.
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