FE Physics
 Formulas & Explanation
 
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Lenses

The optical power of a lens is determined by its focal length.

 

P = 1/f       

 

P  optical power lens in D(ioptre) 

f   focal length in m

P < 0 for concave lenses

 

Lens formula

 

1/f = 1/v + 1/u

 

f   focal length  

v  distance of image

u  distance of object

 

f, v , u : the same unit for length

 

If b<0  then there is a virtual image

With a negative lens : f < 0

                                                                                                

Examples                                 

1.    f = 10 cm     u =15 cm

1/10 = 1/v + 1/15   

0.10 = 1/v + 0.067

1/v = 0.033

v = 30 cm                                                                                    

        Construction : fig 1 

        Two of the three special rays are sufficient    

                                                      

 

                                                                                                                                            fig 1

Lens

 

 

Lens_example

                                                                           

 

            2.   f = 10 cm    u= 4cm                    

1/10 = 1/v + 1/4

0.10 = 1/v + 0.25                                                                 

1/v = -0,15

v= - 6.67 cm (virtual image)

       Construction:   fig 2 

 

 

           

 

 

                                                                                                   

 

                                                                                                                                             fig 2

 

Lens_example_3

                                                                                                                                        

3.  f= - 10 cm (negative lens!) 

     u = 15 cm                         

   

     1/-10 = 1/v + 1/15

-0.10 = 1/v +0.067

      1/v = - 0.167

      v = - 6.0 cm (virtual image)

      Construction:  fig 3

 

 

 

 

                                                                                                                                              fig 3                                                                                    

 

                                                                                                     

 

Magnification

Magnification = height image/height object

M = II’/OO’= - v/u

 

 

M < 0    inverted image

M > 0    upright image

0<M< 1 image smaller than object 

M>1 image larger than object

                        

                   

 

 

Calculation magnification

Example 1 (see above)    M =- v/u =     - 30/15  =  - 2.0 x      II’= 2.0 x  OO’     inverted image  

Example 2                          M = -v/u  = - (-6.67/4) =   1,7 x      II’=  1,7 x OO’     upright image 

Example 3                          M = - v/u = - (-6.0/15) =   0,4 x      II’ = 0.4 x OO’     upright image