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Photometer
Brief description
A photometer is an instrument designed to measure luminous intensity, illuminance, or optical transmission by comparing the brightness produced by an unknown light source with that of a standardized luminous reference. Pioneered by Count Rumford (shadow photometer) and Robert Bunsen (grease-spot photometer), visual photometers applied the inverse-square law of illumination to quantify human lighting, evaluate combustible fuel efficiency, and monitor astronomical brightness.
Use / Function
- Luminous Intensity Measurement: Quantifying the candlepower of artificial lights (candles, gas lamps, incandescent bulbs) relative to standard sources.
- Lighting Efficiency Evaluation: Comparing the light output per unit of combustible fuel or electrical power consumed.
- Optical Absorption & Density: Measuring the transmittance and opacity of colored glass, liquid solutions, and photographic plates.
- Astronomical Photometry: Quantifying the visual magnitudes and light curves of variable stars.
Operating principle
- Inverse-Square Law of Illumination: The illuminance ($E$) on a surface is inversely proportional to the square of its distance from a point light source ($E = \frac{I}{r^2}$).
- Visual Comparison: Two light sources—a known standard and an unknown test source—illuminate opposite sides of a comparison screen placed along a graduated optical bench.
- Equilibrium Point: In Bunsen’s design, a translucent spot made by treating paper with melted beeswax appears darker than the opaque surround when lit from the front, and brighter when lit from behind.
- Disappearance Condition: When both sides of the screen receive equal illuminance ($E_1 = E_2$), the translucent spot visually matches the surrounding paper and disappears from view.
- Intensity Ratio Computation: Knowing the distances from each source to the screen at balance ($r_1$ and $r_2$), the unknown luminous intensity ($I_1$) is determined directly from the known source ($I_2$) via: $I_1 = I_2 \left(\frac{r_1}{r_2}\right)^2$.
How to create it
- Construct Optical Bench: Mount a rigid, straight wooden rail at least 2 meters long, graduated with millimeter and centimeter markings.
- Prepare Bunsen Screen: Take a sheet of clean, unglazed white paper and apply a single drop of melted beeswax or paraffin wax to the center, creating a crisp translucent circular spot roughly 1–2 cm in diameter.
- Enclose Screen Carriage: Mount the paper screen inside a small wooden viewing box sliding freely along the bench rail.
- Install Inspection Mirrors: Position two small mirrors or prisms inside the box angled at 45 degrees on either side of the screen, allowing an observer to view both sides of the paper spot simultaneously through a single front aperture.
- Set Up Standard Lamp: Mount a standardized candle (e.g., standard spermaceti candle) or regulated flame lamp at one fixed end of the bench.
- Position Test Source: Mount the lamp or candle under evaluation at the opposite end of the bench, darken the room, and slide the carriage until the wax spot blends into the paper from both perspectives.
Materials needed
- Essential: Heavy white Paper, pure Beeswax or paraffin, seasoned Wood for the graduated bench rail and sight box, silvered Glass for the two viewing mirrors.
- Tools: Carpenter’s plane, graduated rule, fine knife, wax dropper, spirit level.
- Substitutes: Pure vegetable oil or animal fat can replace beeswax to form the translucent spot; a white plaster rod (Rumford screen) can be used for shadow photometry.
Variants and improvements
- Rumford Shadow Photometer: Compares the darkness of shadows cast on a white screen by an opaque rod from two separate light sources.
- Bunsen Grease-Spot Photometer: The classic translucent wax-spot design with dual mirrors for simultaneous bilateral observation.
- Lummer-Brodhun Photometer: A high-precision optical version using a pair of right-angled prisms with central contact discs to provide adjacent concentric visual fields.
- Photoelectric Photometer: A 20th-century instrument using light-sensitive selenium cells or phototubes to measure current output without subjective human eye comparison.
Limits and risks
- Color Difference Discrepancies: Comparing light sources of different color temperatures (such as cool daylight and warm candlelight) introduces perceptual errors for human observers.
- Stray Reflections: Stray light bouncing off room walls, ceilings, or table surfaces distorts illumination readings unless thoroughly baffled in a black-painted darkroom.
- Standard Source Fluctuation: Combustion candles and gas flames drift in luminous intensity due to wick trimming and drafts, demanding frequent recalibration.