Simple lens model

Simple lens model

The "Simple Lens" model describes a simple optical system consisting of a convex lens collecting light from a monochromatic light source and forming an image of that source. The lens is assumed to be a "thin" lens , i.e. one whose focal length is much larger than its diameter. In the particular solution shown below, 200 nm radiation from a source with a radiance of 0.01 watts sr^-1 cm^-2is collected by a lens with a refractive index 1.6, area of 1 cm² and radii of curvature 10 cm, positioned 16.6 cm from the source.

A print-out of the "variable sheet" is shown below. It lists each variable in the model and the units in which its value is displayed. Additionally, alternative units for each variable are given in parentheses in the Comments column. The relationships between the units are defined by the Unit sheet (not shown).

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St Input     Name    Output    Unit      Comment                                
   200       lambda            nm        wavelength of light (nm, A, 痠, cm)    
             freq    1.5E15    Hz        frequency (Hz)                         
             E       143.24584 kcal/mole energy (Joule, erg, eV, kcal/mole)     
             v       50000     cm-1      wavenumber (cm-1)                      
             f       8.3333333 cm        focal length of lens (cm, m, in)               
   16.666667 S1                cm        source to lens distance (cm, m, in)    
             S2      16.666667 cm        lens to image distance (cm, m, in)     
             M       1                   Magnification factor                   
   1.6       n                           refractive index of lens material                
   10        R1                cm        radius of curvature 1 (cm, m, in)      
   10        R2                cm        radius of curvature 2 (cm, m, in)      
   1         A                 cm2       area of lens (cm2, mm2)                
             D       1.1283796 cm        diameter of lens (cm, m, in)           
             omega   .0036     steradian solid angle collected (steriadians)    
             Fnumber 14.770443           effective F-number of optical system   
             Flens   7.3852213           F-number of lens itself                
   .01       Bs                W/Sr-cm2  source radiance (watts steradian-1 cm- 
   1         As                mm2       Source area viewed (cm2, mm2)          
             Phi     .00000036 W         Light flux incident on lens (watts)    
             Ai      .01       cm2       effective area of image of source      
             Ei      3.2268E-5 W/cm2     Image irradiance (watts/cm2)           
             FotFlux 3.6221E11           Photon flux (Photons/sec) on lens      
             ImgFlux 3.2466E11           Photon flux (Photons/sec) at image     
             rho     .05325444           reflectance of one air interface       
             Tf      .89632716           Overall transmittance of lens
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This is the Rule sheet. It gives the equations that define the relationships between the variables.

S Rule                                                                          
* lambda = 1/v             ' Definition of wavenumber                                           
* E = (6.626E-34)*freq     ' Energy of photon                                     
* freq = (3E10)/lambda     ' speed of light = 3E10 cm/sec
* 1/f=(1/S1)+(1/S2)        ' Thin lens equation                                    
* M=S2/S1                  ' Magnification = (image length)/(source length)                      
* 1/f=(n-1)*(1/R1+1/R2)    ' Lensmaker's equation
* A=3.14159*(D/2)^2        ' Definition of area
* omega=A/S1^2             ' Definition of solid angle
* Fnumber=S1/D             ' Definition of "F" number of system
* Flens=f/D                ' Definition of "F" number of lens
* Phi=Bs*omega*As          ' Relation between flux and radiance
* Ai=As*M^2                ' Image area (cm2)
* Ei=Tf*Phi/Ai             ' Image irradiance, including reflectance loss
* FotFlux=Phi/E            ' Photon flux incident on lens 
* rho=((n-1)/(n+1))^2      ' Reflectance at normal incidence
* Tf=(1-rho)*(1-rho)       ' Overall transmission of two surface/air boundaries
* ImgFlux=Tf*FotFlux       ' Photon flux at image, including reflectance loss
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Download the Simple Lens model.

How to use an existing TK Solver model

1. From the Finder, double-click on the icon of the model, or if you are already in TK Solver, use the Open command (Apple-O) as usual. Click on Reset on the dialog box, then select the desired model file.

2. For each known quantity:

a. Under the "units" column, enter the units in which you intend to use for that variable, if different from the units already there.

b. Under the "input" column, type in the value of that quantity.

3. Type (Apple =). Any unknown quantities which can be calculated from the known quantities will be computed and displayed in the "output" column in the units specified in the "units" column.

[RETURN] to Chem 623 home page.

T. C. O'Haver, Chem 623, 1994