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Thus, a +1.0 diopter pair of reading glasses is just perfect for our needs. To quickly build a projection system, simply place the glasses and the projection screen a metre apart. Adjust the glasses and the screen until a clear image of the Sun is obtained.

Optics is a precision science. Rather than get everything measured out to the last decimal point, it's easier to plan for some way of moving the lens, so that the best focus can be achieved on the fly.

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PInhole projectors are easy to construct, requiring only a screen, a pinhole, and usually some form of shielding to block out ambient light. The problem with pinhole projectors is that the images formed are often underwhelming. With a pinhole-to-screen distance of about 30 cm, you'll get an image of the Sun that's barely 2 mm across.

Solar eclipses are rare astronomical events which are exciting to watch, but require some form of equipment for safe viewing. Even if most of the Sun is obscured, it still emits enough light, particularly ultraviolet light, that can cause permanent damage to the eyes.

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For an object at infinity, the angular size of the image is the same as the angular size of the object. The angular size of the Sun is about 0.5 degrees, hence the angular size of the image is also 0.5 degrees. Knowing the distance at which the image forms, and the angle it subtends, you can calculate its actual size. No need for trigonometry when you have a long focal length and a small angular distance - simply use the small angle approximation (distance x angle in radians), and you'll find that the Sun's image from a +1.00 diopter lens is approximately 9 mm across.

Identify one end of the cardboard tube as your projection screen. Glue the matte black paper to the inside of the tube there, to absorb unwanted reflected light.

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The Sun is essentially an object at infinity. This means that rays coming from the Sun will converge towards the focal point of the lens, which is at a distance equal to the focal length away from the centre of the lens. Thus, for a +1.00 diopter lens, the Sun's image will be 1 metre away from the lens. A +2.00 diopter lens has a focal length of 50 cm, so the image will appear 50 cm away.

So, while a lens with a higher power requires a shorter projection distance, the image formed is correspondingly smaller. This is also where things start running into the danger zone - you're focusing all that solar energy into a smaller and smaller area. At some point it'll get hot enough to burn your projection screen (think magnifying glass and Sun).

Tape the lens over the aperture. This is a good point to try out the lens/aperture assembly, to see if the image of the Sun is neither too bright nor too dim.

This Instructable demonstrates a way to safely view the a solar eclipse using a lens-based projection method. It also works for (large) sunspot watching. All you really need is a pair of dollar store reading glasses, some cardboard, and duct tape!

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And that's it! To use the viewer, aim the lens end at the Sun. Use the shadow of the viewer to guide your aim - find the position that gives the smallest shadow. Slide the sleeve to get a sharp focus. Prop it up or use a tripod for a steadier setup.

Most eclipse sites recommend using special eclipse glasses, which are often made from Mylar that blocks off most of the Sun's light. If these are not available, the recommendation is often some form of pinhole projection method.

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However, when a lens is used instead of a pinhole, a clear bright image can be obtained. The trick is finding a lens that has a long enough focal length to produce a large image.

Cut out some cardstock that fits over the end of the sleeve. This forms the lens holder. In the centre of this lens holder, cut out a small aperture, about 1 cm in diameter. This aperture reduces the amount of light landing on the screen, producing a image that is not too glaring to look at.

The image size can be increased by making the pinhole-to-screen distance longer. Doubling this distance will double the diameter of the image, but its brightness will be reduced by a factor of 4, as light intensity is inversely proportional to the square of the distance. So, while in theory you can make a huge image with a pinhole projector by having the screen really far away, the image be so dim that it'll be hard to make out anything.

Fortunately, such lenses are easily available, in the form of cheap dollar store or drug store reading glasses. These glasses are specified in diopters, which is simply the inverse of its focal length, f. Reading glasses typically come in the range of +1.0 to +3.5 diopters, which translates to focal lengths of 1 metre down to about 30 cm.

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Using the cardstock, construct a sleeve that fits snugly around the tube. This sleeve should not be too loose, some effort should be required to slide it back and forth along the tube.

Once you've got a lens/aperture assembly you're satisfied with, tape it over the sleeve, then slide the sleeve back onto the tube.

Of course, this isn't good enough for us. The image formed in this way is often too bright, and it gets annoying when people walk between the glasses and the screen. You also wouldn't want anyone sticking their head in the beam path and looking at the Sun, through the glasses.

First, a bit of simple geometrical optics. Reading glasses use convex lenses to achieve their corrective action, so you can simply use the basic rules of geometrical optics to work out where and how big the final image will be.