\[\frac{1}{f}=\frac{1}{d_o}+\frac{1}{d_i}\]
Variables
ffocal length (m)
doobject distance (m)
diimage distance (m)
Description
What is this formula?
This formula relates the focal length of a thin lens to the object distance and image distance. It is one of the fundamental equations of geometrical optics and determines where an image forms.
When to use it
Use this formula when analyzing converging or diverging lenses, camera systems, microscopes, telescopes, and image formation problems.
Example
Given:
do=0.30 m
f=0.10 m
Formula:
1/f=1/do+1/di
Rearranged:
di=(f×do)/(do−f)
Substitution:
di=(0.10×0.30)/(0.30−0.10)
Result:
di=0.15 m
Applications
- Camera optics
- Eyeglasses design
- Microscopes
- Telescopes
- Image formation analysis