Optimizing Projector Design: Calculating Lens Distances & Magnification Factors

[sharp81]

hi,
i am in need of help pretty quickly here.i will have to design a projector design using a fresnel lens and the projection lens.i need to find and derive the equations for the lenses and calculate the distances between the lenses and the lens and the screen.
this is what i require to have :
d1 - distance from the light source to the fresnel lens
d2 - distance between the fresnel and the projection lens
d3 - distance between the projection lens and the screen
f1,f2 - focal lengths of the fresnel lens
f3,f4 - focal lengths of the projection lens
In my case i know the values of the focal lengths and the distance between the light source and the fresnel lens.

i will have to find d2 and d3. also i need to find the net magnification factor for the light source which will be my object.
any help will be greatly appreciated.
harish

 

[Valerie Park]

The equations you need to calculate the distances and magnification factor are as follows: 1. Magnification Factor = f3/f2 2. d2 = (f1*f3)/(f2-f1) 3. d3 = (f2*f4)/(f3-f4) Using these equations and the given data, you should be able to find d2 and d3. For example, if f1 = 5 cm, f2 = 10 cm, f3 = 15 cm and f4 = 25 cm, then d2 = (5*15)/(10-5) = 22.5 cm and d3 = (10*25)/(15-25) = 166.67 cm. In this case, the net magnification factor will be 3 (f3/f2 = 15/10 = 3). Hope this helps!

 

[Graeme Robinson]

Hello Harish,

Thank you for reaching out for help with your projector design project. It sounds like you have a clear understanding of the variables involved and what you need to calculate. To help you with your design, I would suggest using the thin lens equation and the magnification equation, which are commonly used in optics and lens design.

The thin lens equation is: 1/f = 1/d1 + 1/d2, where f is the focal length of the lens and d1 and d2 are the distances from the lens to the object and image, respectively. You can use this equation to find the distance between the fresnel lens and the projection lens (d2) by rearranging it as d2 = (f1*f2)/(f1+f2).

Similarly, you can use the magnification equation M = -d2/d1 = f2/f1 to find the magnification factor of the light source. This equation relates the distances and focal lengths of the lenses to the magnification of the image.

To find the distance between the projection lens and the screen (d3), you can use the same thin lens equation, but this time using the focal lengths of the projection lens (f3 and f4) and the desired image distance (d3). Rearrange the equation as d3 = (f3*f4)/(f3+f4) to solve for d3.

I hope this helps you with your design. Good luck with your project!