It's not exactly true, though. You can actually look at the sun briefly without burning a hole in your retina. A little longer and you will temporarily wipe out the part of your retinas that the image of the sun fell on. Longer than that and that part of your retina will be permanently out of operation.
The problem is that everyone is different. If someone tells you that they looked at the sun for three seconds without lasting effects, your eyes might be able to take only one second. And that is why I suggest that you never look directly at the sun.
Your vision is precious. Don't risk it.
The image of the sun on the light sensitive part of your camera will also destroy it in a very short time.
But there are ways to observe the sun. You can get a blurry image with little cost. It's acceptable for viewing solar eclipses but not for detailed solar observation. For that, you will have to put out some cash.
I only do the inexpensive stuff here. This is my solar observation tool kit.
The most common means of viewing the sun is with a pinhole. That's what the silver rectangle is. I cut a small square out of two pieces of card stock (index cards are perfect, and folded a piece of light weight aluminum foil over one side. In the middle of the square hole, I used a pin to punch a tiny hole in the foil. To punch the hole, I placed the foil side down on a hard surface (I used a craft cutting board but a marble table top or similar surface will work fine) and pressed a pin point against it.
Holding the pinhole over another card and using it to project the sun's image, I got the following.
It's...uh, that tiny dot in the center of the black circle...you might have to enlarge the photo. You can move the pinhole nearer and further from the card. When you move it away, the dot gets bigger. The problem is that it also gets dimmer.
A large hole will provide a larger image but it will be dimmer and fuzzier. The main problem is that light from the surrounding area will wash out any details.
I have two inexpensive (but very cool) science kits that include pinhole projects. The white box is from the ScienceWiz: Light kit. I cut a hole, about a half centimeter, into one wall of the box opposite the side that isn't there (the box only has five sides. The missing side has been replaced with wax paper.) When I aim the pinhole at the sun, the sun's image is cast onto the wax paper. The box shields the image from glare.
The hole wasn't very round so the image came out sorta whompsided. A paper punch would have given me better results. But, if you do this project, don't expect to see a lot of details. The big hole is better suited as a pinhole camera for landscapes.
I got a much nicer image by replacing the lenses from a simple refractor telescope kit (the Project STAR telescope bought from Home Science Tools) with a foil pinhole (I punched a pushpin completely through the foil to create a larger pinhole) at one end and wax paper at the other (the kit instructions tell how to build the pinhole tube).
With a pinhole tube, you can slide the telescoping cardboard tubes in or out to sharpen the image.
You can also use telescoping mailer tubes to create a pinhole tube.
A second way to inexpensively look at the sun is to use a #14 welder filter. It cuts out more than 99% of the sun's light. Eclipse glasses (which are really inexpensive) do much the same thing. Old science kits suggest that you use a candle to coat one side of a microscope slide with soot to create a solar filter. The problem is that it's very easy to scratch away a tiny section of soot and that's all the sunlight you need to blast your retina or a camera CCD into oblivion...not a good idea.
The second photo is zoomed. Zooming with a digital camera won't give you any more details but it will make the image larger (and fuzzier).
The pinhole phenomenon produces an interesting effect during an eclipse as spaces between leaves on trees act as pinholes to cast images of the sun onto the ground.
These methods will give you great images of an eclipse. (See the blog for August 21, 2017 for images of the last total eclipse in Colorado.) For observing the sun in detail, you need something that will either project a cool image (a lens will just start fires), or a special filter. You can buy a special telescope called a sunspotter for a little over a hundred dollars. With it, you can see sunspots and flares.
You can use a sun filter (or welder filter) with a scope but the filter has to go over the objective lens and it has to cover the objective completely. You can get a sun filter for most telescopes and some binoculars. Here's my Carson telephoto lens on my smartphone with a #14 welder filter between it and the sun.
Here, you can see the sun's corona. The bubble at the upper right of the image is an artifact, but you can just see a solar flare below it. This is about the best I can do with my set up. Any sunspots would be masked by the general brilliance of the sun's image.
You can project the image if the sun through a scope but keep in mind that things (the scope's optics, the surface you project onto, whatever's under that...) will quickly heat up.
If you want to seriously get into solar observation, the sunspotter telescope is one way to go.
Another is an H alpha filter. It filters out all light except a very narrow band from the hydrogen spectrum (thus, it's name). It's expensive but it will show you incredible solar details. It will also block light pollution in urban settings.
Professional astronomers use radio, ultraviolet, and infrared telescopes (in addition to their regular telescopes) to get their solar images. For a lot of cool images of our hot sun, check out Wikipedia (https://en.m.wikipedia.org/wiki/Sun).
As a curious astronomy observer, you don't have to spend a lot of money to watch space and most of the inexpensive pieces of equipment are also very portable so you can easily carry them on the trail. With a little more money, you can turn astronomy into a hobby that can grow to any level.
The sun is a fascinating object to track but be safe and enjoy it.
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