You're going to have friends over to watch a movie when armed robbers enter your home. You defeat them easily, of course, with your ninja skills and Instructables-based weapons, but in the process your TV is damaged, now your movie night is ruined! Well have no fear, now with a few simple parts you have lying around and a little bit of physics you can save the day. I was in a similar situation once, with only a few differences - my friends were moving out and thus had no TV, but we were destined to watch a horror movie, as is custom. And so using all the knowledge I could muster from high school physics, I came up with this simple design.

Basically, we will be using the magnifying glass to focus the light from the laptop's screen to form an image.

This is designed to be used either for personal use, or for educational purposes, to illustrate the concepts behind thin-lens optics in a way that is accessible, interesting, and cheap. The brightness of your projection will greatly depend on the brightness of the image you are projecting and the optics you are using. I will address both of these issues in good time.

Step 1: Materials

Ok, now down to brass tacks (Note: actual brass tacks may or may not be required). Let's take inventory:

1. Laptop or computer monitor, the brighter the better.
2. Storage tub
3. Magnifying glass
4. Measuring tape
5. Scissors
6. Paper and pencil
7. Calculator
8. Cardboard

That's about all that's required for making the projector. However, for the calibrations, I suggest some additional materials:

9. A directional light source, like a desk lamp
10. String
11. Something translucent with writing or pictures on it, like a newspaper clipping or a receipt.

Step 2: Calibrations

You've heard it many times before: "Can it wait for a bit? I'm in the middle of some calibrations." Well now you are going to do some calibrations! That is, we need to acquire some data to determine the Focal Length of our lens. Don't know what a focal length is? That's okay, we'll cover it in the next section during our calculations. Generally speaking, it is a quantity related to the distance at which the lens places an image in focus.

To get at this quantity, we need to set up a small projector:

1. Attach the object to be projected to the light source, as flat as possible, but leave enough room for heat to escape, or you will have a fire on your hands (or on your table).

2. Hang the magnifying glass around a foot in front of the light source so that it is in the beam path. Mine was at 20.3cm (8in.). Measure the distance from the canter of the lens to the object. This is do, the distance to the object.

3. Tape a piece of paper to a book or some other object to serve as a screen. Ensure that it is high enough to be in the beam path.

4. Place the screen some distance away from the lens. Mine was at 90.17cm (35.5in).

5. Turn off the lights and turn on the light source.

6. Move the screen back and forth until the image being projected is in focus. Measure the distance from the center of the lens to the screen. This will be di, the distance to the image.

7. Choose a feature on the screen that you can measure. Record this number as S2, the size of the image. Measure this same feature on the original object and record this as S1, the size of the object.

8. Turn off the light and disassemble the setup. The calibrations are done and you can go save the galaxy.

Step 3: Math

Now that all your attention are belong to us, we can sneak in some math.

The values we just collected from our calculations will be used in the Thin Lens Equation, which is a simplified version of the Lens Maker's Equation. Technically, our lens isn't extremely thin, but the approximation does a pretty good job, and it avoids a lot of math and measuring. Based on the data we collected, we are going to calculate the focal length of the lens, which is an intrinsic property of the lens based on the radius of curvature and tells us how much the lens bends light. We will calculate the focal length by two methods, and use the average of the values we obtain (in an attempt to minimize error).

See the first image for both methods

Method 1: The Thin Lens Equation
The thin lens equation is fairly simple, and relates di, do, and f. By my calculations, f =16.57cm.

Method 2: Magnification
The magnification of the lens is often an important property, and is simply the ratio of the image size to the object size. Here, this ratio has a negative sign because the image is upside down. Magnification can also be related to f and do. This calculation leads to a focal length of f = 16.64.

These calculations are in good agreement, with only 0.4% difference between them.

See the second image for the next calculation

Now that we have the focal length, we can determine the di and do for our actual projector. Here, I set di as 177.8cm (5.83ft). Why use such a nice even number, you ask? Well, it just makes the calculations so easy! I just based this number on how far my table was from the wall. You can choose any number you want, but there are a few considerations:
1) The smaller your di, the smaller, but brighter your image will be
2) Your do must be such that the lens will still fit in the box

Generally 150-180cm (5-6ft) is a good distance for di, as the image will be large but still visible. Once you know your do and di, you are ready for the next step!

I have also included a ray diagram to show how a convex lens bends the light from an object to form a real image. This will only occur if the object is outside of the focal length of the lens. Otherwise, a virtual image is produced (this is how a magnifying glass is normally used).

Step 4: Assembly

Alright, no more math! Now we need to grab that cardboard and cut out a piece that corresponds to the interior dimensions of the storage bin so that it will fit snugly. Depending on your image source, you may need to subtract the thickness of your laptop from one dimension (see the first image).

Now find the center of the rectangle. The simplest way to do this is to draw the diagonals of the rectangle and find their intersection. Then lay down your lens, trace it, and cut out a hole slightly smaller than it, so the lens fits snugly. Mark out the appropriate location in the storage bin for the cardboard based on your calculations (do), and place it in there. Place your projector at the appropriate distance away from the screen/wall (di), and remember to measure from the center of the lens!.

Step 5: Tweak and Enjoy

You are nearly ready to be the most awesome person at the party! First, a few things:

1) We are using a single lens, so the image will be upside down. Thus, you will need to rotate the image on your screen. This can be done from the graphics control panel for whatever graphics card you use. I use Nvidia, so I open the Nvidia control panel and rotate the display.

2) The lens won't capture all of the light from your screen, so you want to make it as bright as possible. You can turn the brightness all the way up, but that may not be enough. I went back into the Nvidia control panel, maxed out the brightness, increased the gamma, and increased the digital vibrance (to compensate for gamma's effect on color).

3) The calculations were based on the thin lens APPROXIMATION, so you may have to slightly adjust the distances. Changing the distance between the lens and the laptop only slightly will greatly alter the focus distance, so use this for gross adjustments (if the image is very blurry). Moving the whole projector will achieve fine adjustments. However, the approximation is surprisingly accurate, so you shouldn't have to tune the system too much.

4) Turn out the lights and get cracking! If your laptop is quiet, consider hooking up speakers to your headphone ports. You will also be using a lot of power, so be sure to plug your computer in.

I hope you enjoyed my first Instructable. I have been reading all of your tutorials for years, but now I have something of my own to contribute.