A difficult geometric problem
Finding the reflection point for a spherical mirror leads to a fourth-degree equation. Ibn al-Haytham treated it geometrically.
25 / ANTIQUITY TO THE RENAISSANCE
Hasan ibn al-Haytham
You see a candle’s reflection on a polished ball. Exactly where on the ball does its light bounce into your eye?
Explore the mathematics ↓
01 / ALHAZEN’S PROBLEM
Where must the light bounce?
Drag the bounce point over the ball until the bounced light enters the eye.
At that point the radius, the ball’s upright, makes equal angles with the light coming in and going out.
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THE IDEALight leaves at the same angle to the upright as it arrives. On a ball the upright is the radius, so the bounce point is where the radius splits the candle–eye angle in half.
The person behind the ideas
- Worked on optics, geometry and number theory.
- Wrote the influential Book of Optics.
- Studied the reflection problem now called Alhazen’s problem.
More of the mathematics
Light enters the eye
His optical work helped explain vision in terms of light reaching the eye from objects.