FE Physics
Formulas & Explanation     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  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 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