Photometry
Simple Explanation
Photometry measures how bright light appears β the illuminance (E) falling on a surface from a point source follows an inverse-square law, E=I/dΒ², so a light source appears four times dimmer at twice the distance.
Why Do We Need It?
This inverse-square relationship governs everything from choosing the right light bulb for a room to how astronomers estimate the true brightness of stars from how dim they appear across enormous distances.
Formula
Illuminance from a Point Source
E = I/dΒ²
The illuminance (brightness of light falling on a surface) from a point source falls off with the square of the distance β moving twice as far away makes a light source appear four times dimmer.
- E
- β illuminance, in lux (lx)
- I
- β luminous intensity of the source, in candela (cd)
- d
- β distance from the source, in metres (m)
When to use it: Whenever the brightness of light falling on a surface at a known distance from a point light source needs to be found.
Worked Example
Find the illuminance from a light source
A light source has a luminous intensity of 100 cd. Find the illuminance on a surface 2 m away.
Why Does This Work?
A point source spreads its light equally over an expanding sphere β since a sphere's surface area grows with the SQUARE of its radius (4ΟdΒ²), the same total light energy is spread over an ever-larger area as distance increases, making the light per unit area (illuminance) fall off as 1/dΒ².
Real-Life Example
Why standing farther from a lamp makes reading harder
Reading a book becomes noticeably harder when moving a lamp twice as far away, even though the lamp itself has not changed.
Doubling the distance to the lamp reduces the illuminance on the page to just one-quarter of its original value, by exactly this inverse-square law.
Practice
A light source has a luminous intensity of 60 cd. Find the illuminance on a surface 3 m away.
MediumCommon mistake
Assuming illuminance falls off proportionally with distance (halving at double the distance) β it actually falls off with the SQUARE of the distance (to a quarter at double the distance), a much steeper drop.
Quick Review
- E = I/dΒ² β the inverse-square law.
- Doubling the distance reduces illuminance to one-quarter.
- Comes from a sphere's surface area growing with the square of its radius.