Spherical Mirrors

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Geometric derivation of the magnification formula.


[magnify]

Similar triangles. The magnification formula.

M = hi = di
hodo

Geometric derivation of the spherical mirror formula.



[magnify]

Magnification equation, similar triangles.

M =  hi  =  di  =  f
ho do do − f

cross multiply, distribute, collect like terms.

di(do − f)  =  dof
dido − dif  =  dof
dido  =  dif + dof

Divide by didof.

dido  =  dif  +  dof
didof didof didof

Simplfy. The spherical mirror formula.

1 = 1 + 1
fdodi

uh huh, fried taters

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