Designing a Basic Overhead Projector: Physics, Calculus, and Mirrors

[kdinser]

For a class, I need to design a basic overhead projector. I know a little bit about optics from an algebra based physics class I took a while back, but I don't remember most of the specifics, such as what kinds of lenses flip objects before and after their focal points. I'm also not sure what effect the directional mirror will have on the image.

Here's what I've got so far, we get bonus points the more detail we are able to put in so I'm going to toss in some calculus dealing with the reflective properties of a parabola rotated about it's axis. I'll have a concave mirror in the bottom, the mirror's dimensions will be provided by rotating a parabola around it's axis. A light source will be located at it's focal point, according to what I remember from physics and my calc book, this will direct the light parallel to the axis of the parabola. At the top of the base I'll have a fresnel lens. This will angle the light to a focal point. At the head of the device I'll have a plano convex lens, rounded side down to collect the light and convert it back to parallel before striking the mirror and going on to the screen.

Sound right so far?

My question is, do I want the focal point of the first lens to be between the lenses or past the second lens? Also, I'm having a hard time visualizing what effect the mirror is going to have on the image, turn it upside down? make it backward?

Thanks for any help.

 

[member 553083]

Yes, that sounds right so far. The focal point of the first lens should be between the lenses, and the mirror will flip the image horizontally (i.e. left to right).

 

[wais]

Your design so far seems to be on the right track. A basic overhead projector consists of a light source, lenses, and mirrors, all working together to project an enlarged image onto a screen. In order to understand the physics behind this, let's break down the components and their functions.

First, the light source. This can be a lamp or LED, positioned at the focal point of the concave mirror. As you correctly stated, the light will travel parallel to the parabola's axis after being reflected by the mirror. This is because the parabola's shape allows all incoming rays to reflect and converge at the same point, creating a focused image.

Next, we have the fresnel lens. This lens is made up of a series of concentric circles, which act as prisms to bend and focus the light even further. The focal point of this lens should be between the two lenses, as this will help to create a clear and magnified image.

Then we have the plano-convex lens. This lens is responsible for collecting the light from the fresnel lens and converting it back to parallel rays before it hits the mirror. This is important because the light needs to be parallel in order for the mirror to reflect it and project a clear image onto the screen.

Now, let's talk about the mirror. The concave mirror will flip the image upside down and backward. This is because the light rays are being reflected off the mirror and redirected towards the screen. So, if you place an object on the projector, it will appear upside down and backwards on the screen. This is why you need to position the object correctly on the projector to ensure it appears correctly on the screen.

In terms of the mirror's dimensions, using a parabola rotated around its axis is a good approach. You can use calculus to determine the exact dimensions of the parabola in order to create the desired focal point for the light source.

Overall, your design seems to be well thought out and incorporating calculus to determine the reflective properties of the parabola is a great addition. Just remember to position the lenses and light source correctly and take into account the mirror's effects on the image. Good luck with your project!