Cheap Educational Scope

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;

%% define all constants
%all units are in meters
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
%Thin lens equation. Dndv is a virtual image, so it is negative. 
Devi = 1/(1/Fo - 1/(-Dndv)); 
%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)
Devi = 29.2mm (Eye-lens to real image distance)
Lt = 134.8mm(optical tube length, Do + Devi)
Moptimal = 16.5
Mt = -16.7

2013 Jasper Nance KE7PHI