Photometers
Make two screens equally bright and the distances tell you which lamp is stronger.
Lesson at a glanceShow the key points
- Two screens lit at equal angles by two sources look equally bright when I₁/d₁² = I₂/d₂², so I₁/I₂ = d₁²/d₂² (22.7).
- Bunsen photometer: a paper with a grease spot between the two sources on an optical bench; two mirrors show both sides of the spot at once.
- Slide one source until both sides look equally bright, then measure d₁ and d₂.
The eye is a poor judge of how bright something is, but an excellent judge of whether two things are equally bright. Photometers use that talent to compare light sources.
The principle
Two screens sit side by side; one is lit only by source S₁, the other only by S₂, both at the same angle. Move the sources until the screens look equally bright. Then their illuminances are equal:
Bunsen’s grease-spot photometer
An optical bench carries three stands on a rail with a metre scale. The middle stand holds white paper with a grease spot; the other two carry the sources S₁ and S₂. Two plane mirrors behind the paper let you see both sides of the spot at once.
The grease spot lets some light through. When one side is lit more strongly, the spot looks darker than the paper on that side and brighter on the other. Keep one source fixed and slide the other until the spot looks the same on both sides: the illuminances match. Measure d₁ and d₂ and use the formula above.
A 40 cd lamp and an unknown lamp balance a photometer when they are 0.80 m and 1.20 m from the screen. Find the unknown intensity.
- 1Equal brightness of two screens means equal illuminance: I₁/d₁² = I₂/d₂².
- 2Bunsen photometer: a grease spot on paper between the two sources, viewed in two mirrors; balance when the spot vanishes against the paper.
Check yourself
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