AcademyGeometric Optics
Academy
The Eye
Level 1 - Physics topic page in Geometric Optics.
Principle
The eye focuses light on the retina by changing optical power.
Notation
\(P\)
optical power
D
\(f\)
effective focal length
\(\mathrm{m}\)
\(s\)
object distance
\(\mathrm{m}\)
\(s'\)
retina distance from eye lens system
\(\mathrm{m}\)
\(N\)
standard near point distance
\(\mathrm{m}\)
\(P_{\mathrm{lens}}\)
corrective lens power
D
Method
Derivation 1: Optical power
Eye optics are often described by diopters.
Power
\[P=\frac{1}{f}\]
Thin-lens model
\[\frac{1}{s}+\frac{1}{s'}=P\]
Derivation 2: Accommodation
The retina position is fixed, so focusing different object distances requires changing optical power.
Distant object
\[s\rightarrow\infty\Rightarrow P\approx\frac{1}{s'}\]
Near object
\[P=\frac{1}{s}+\frac{1}{s'}\]
Accommodation change
\[\Delta P=\frac{1}{s_{\mathrm{near}}}\]
Rules
Optical power
\[P=1/f\]
Eye focus
\[\frac{1}{s}+\frac{1}{s'}=P\]
Standard near point
\[N=0.25\,\mathrm{m}\]
Examples
Question
Find the power of an eye modeled with effective focal length
\[17\,\mathrm{mm}\]
for distant objects.Answer
\[P=\frac{1}{0.017}=59\,\mathrm{D}\]
Checks
- Myopia is corrected with diverging lenses.
- Hyperopia is corrected with converging lenses.
- Diopter power uses focal length in meters.