Difference between revisions of "Cheap Educational Scope"
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(Edited code to be much more readable and also added a calc for eyepiece2real image distance) |
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==The Cameras== | ==The Cameras== | ||
| − | Walmart! Full lens diameter not usable, need to stop down with a 3mm stop | + | Walmart! 33mm focal length lenses. Full lens diameter not usable, need to stop down with a 3mm stop. |
==The 2-lens Matlab Model== | ==The 2-lens Matlab Model== | ||
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<pre> | <pre> | ||
clear; | clear; | ||
| + | clc; | ||
| + | |||
%all units are in meters | %all units are in meters | ||
| − | Fo=. | + | %define all constants |
| − | Fe=. | + | 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 | Dndv = .25;%.25 is the distance of "nearest distinct vision" in humans | ||
| − | + | Aacuitydegrees = 2/60; %human visual foveal acuity is 2 arcminutes | |
| − | Di = 3.2*Fo; %random guess of 4 | + | Wgreen = 550e-9; %wavelength of green light is 550nm |
| − | + | ||
| − | %M=f/(f-Do) for distance to the object | + | %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 = -Di/Do | ||
%M = (f-Di)/f for distance to the image | %M = (f-Di)/f for distance to the image | ||
Mo = (Fo-Di)/Fo; | Mo = (Fo-Di)/Fo; | ||
Do = -Di/Mo; | 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); | Theta = atand((0.5*Pe) / Do); | ||
NA = sind(Theta); | NA = sind(Theta); | ||
| − | Resolution = | + | Resolution = Wgreen/(2*NA); %green light resolution |
| − | |||
| − | |||
Dsep = 2*sind(Aacuitydegrees/2)*Dndv; %lowest resolveable distance at Dndv | Dsep = 2*sind(Aacuitydegrees/2)*Dndv; %lowest resolveable distance at Dndv | ||
| − | Moptimal = (2*NA*Dsep)/ | + | Moptimal = (2*NA*Dsep)/Wgreen %550nm is green light |
| − | + | ||
</pre> | </pre> | ||
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----------------------------- | ----------------------------- | ||
Do = 46.5mm (object-lens distance for an in focus image) | Do = 46.5mm (object-lens distance for an in focus image) | ||
| − | Lt = | + | Lt = 143.6mm(optical tube length) |
Moptimal = 17.0354 | Moptimal = 17.0354 | ||
Mt = -17.1875 | Mt = -17.1875 | ||
Revision as of 10:24, 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 = 46.5mm (object-lens distance for an in focus image) Lt = 143.6mm(optical tube length) Moptimal = 17.0354 Mt = -17.1875
2013 Jasper Nance KE7PHI
