Difference between revisions of "Cheap Educational Scope"
(Edited code to be much more readable and also added a calc for eyepiece2real image distance) |
m (Updated script results) |
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RESULTS | RESULTS | ||
----------------------------- | ----------------------------- | ||
− | Do = | + | Do = 48mm (object-lens distance for an in focus image) |
Lt = 143.6mm(optical tube length) | Lt = 143.6mm(optical tube length) | ||
− | Moptimal = | + | Moptimal = 16.5 |
− | Mt = - | + | Mt = -16.7 |
</pre> | </pre> | ||
2013 Jasper Nance KE7PHI | 2013 Jasper Nance KE7PHI |
Revision as of 10:42, 17 June 2013
Problem Statement
I needed a quick idea for summer camp educational workshop that was 'sciencey'. I remembered seeing this thingiverse link a while back and sharing it with a friend of mine who is an elementary school teacher. I wanted to do this as a workshop but also to understand the operation behind it as I am ashamed to say that my knowledge of optics is pretty bad...
I also wanted to understand the weak spots of the scope so that older kids could make a more advanced version that would be more capable or easier to use.
The Eye
I first used ray tracing theory to understand the real and virtual image locations. I was hung up very quickly on the fact that without an eye, a virtual image is pretty useless. The eye is an integral part of a microscope!!!
Luckily I found some information on the human eye. Some of the really important ones are
- Visual acuity: 2 arcminutes
- Distance of Nearest Distinct Vision: 25cm (between this and infinity are good places to place your final virtual image)
- Translated visual acuity at the distance of nearest distinct vision: 145µm (wow, my eyes are amazing!!)
- Focal Length of the Eyeball: 2.2cm
Reminder to myself to scan and stick in the raytrace model
The Cameras
Walmart! 33mm focal length lenses. Full lens diameter not usable, need to stop down with a 3mm stop.
The 2-lens Matlab Model
clear; clc; %all units are in meters %define all constants Fo=.033; %objective focal length Fe=.033; %eyepiece focal length Pe = .003; %entrance pupil of 3mm (refine this to include mag effect) Dndv = .25;%.25 is the distance of "nearest distinct vision" in humans Aacuitydegrees = 2/60; %human visual foveal acuity is 2 arcminutes Wgreen = 550e-9; %wavelength of green light is 550nm %Find image/object distances and magnigication of the objective lens Di = 3.2*Fo; %random guess of 4 times (iterative solution) %M=f/(f-Do) for distance to the object (thin lens & def of magnification) %M = -Di/Do %M = (f-Di)/f for distance to the image Mo = (Fo-Di)/Fo; Do = -Di/Mo; %Find iimage/object distances and magnigication of the eye lens Devi = 1/(1/Fo - 1/Dndv); %Thin lens equation %Total length = Obj<->image<->Eyepiece = Obj2image + Image2eyepiece Lt=Di+Devi Me = Dndv/Fe; %Find the actual magnification of the system Mt = Mo*Me %Find the resolution of the system (and the max practical magnification) Theta = atand((0.5*Pe) / Do); NA = sind(Theta); Resolution = Wgreen/(2*NA); %green light resolution Dsep = 2*sind(Aacuitydegrees/2)*Dndv; %lowest resolveable distance at Dndv Moptimal = (2*NA*Dsep)/Wgreen %550nm is green light
RESULTS ----------------------------- Do = 48mm (object-lens distance for an in focus image) Lt = 143.6mm(optical tube length) Moptimal = 16.5 Mt = -16.7
2013 Jasper Nance KE7PHI