# Comparing Light Bulbs

In the early 20th century a clever photometer was invented by John Joly.  One can use this to characterise the light intensity from modern high efficiency light bulbs.

## The Joly Photometer

Two wax or paraffin blocks are put together with an opaque sheet of aluminum foil between them as shown in the following:

The wax blocks can be put into a box with windows to let the light from the light sources shine on the blocks and a third window to observe the relative brightness of the two blocks. When positioned between two light sources, $I_1$ and $I_2$, so that both blocks appear equally bright, the relative intensities of the two light sources can be calculated by the inverse-square law.

$$\frac{I_1}{I_2} =\frac{s_1^2}{s_2^2}$$

## Crude Implementation

Here is a hastily-made version that works even without the aluminum separator sheet or an enclosing box. The two light sources were a 60-watt equivalent led bulb (Philips) on the left and a 60-watt equivalent cfl bulb  on the right.

The led was a “soft-white” bulb, so there was some colour difference between the bulbs, the led was more yellowish. Both claimed about 850 lumens brightness. Brightness comparison was aided by removing the colour saturation from the images.  (Click on the images to enlarge. Then you can see the ruler more clearly.) It is interesting to note that the cfl bulb consumed 12 watts power whereas the led bulb a little more at 13 watts power. One can clearly tell the difference in intensities when the position is varied.  The distance between light sources was 1.5 m in this case.

I found that the blocks appeared to be equally illuminated when the distance was 0.80 to 0.85 m from the left-hand block. This corresponds to the right-hand block being dimmer then the left-hand bulb by between 30% to 70%.

The relationship between $I_2$ to $I_1$ in terms of the equal-intnsity position of the blocks, $x$, when the lights are a distance $L$ apart is given by the equation

$$I_2 = I_1 \left(\frac{L-x}{x}\right)^2$$

Intensity ratio for various block positions, $L$=1500 mm
$x (mm)$ $I_2/I_1$
500 4.00
550 3.00
600 2.25
650 1.71
700 1.31
750 1.00
800 0.77
850 0.68
900 0.44
950 0.33
1000 0.25

## Measurements on real bulbs

I wanted to compare the power usage and light output of some real lightbulbs bought at the store.  As a base to compare with, I used a 60 W (nominal) incandescent bulb with a stated lumen intensity of 620 lumens.  The CFL and LED bulbs both claimed 800 lumen output and nominal 10 W and 9.8 W power respectively.

As you can see from the table the situation is more complicated. The CFL bulb has a much lower light output during the first few minutes of operation, but directionality of the light output is similar to that of the incandescent: uniform.  The LED bulb puts about 3 times more light/steradian in the top than on the side.

Light Bulb Comparisons
Bulb1 Bulb2 Pos Lumen2/Lumen1 Watts1 Watts2
Incandescent CFL (cold) 900 .44 54 9
Incandescent CFL (warm) 700 1.31 54 9
Incandescent LED (top) 500 4.0 54 9
Incandescent LED (side) 700 1.3 54 9
Incandescent Candle 1350 0.012 54 0
LED lamp low Candle 1050 0.18 .6 0
LED lamp med Candle 1200 0.06 1.2 0
LED lamp high Candle 1350 0.012 3.6 0

When power outages occur, people tend to bring out candles. My measurement of a candle output vs the 60 W incandescent bulb showed that the bulb was about 80 times brighter.  This measurement was fraught with error. The percentage error near the end of the range (near $L$) is high: a 5mm error can cause a 20% error in the ratio intensity at 1450 mm. Another problem is that when the Joly photometer is near the candle the wax block on the candle side will melt.

The LED desk lamp ran from a USB connection. It had three positions and had a reflector so that it would only illuminate in one direction covering a limited area. Thus, while the light output measured was similar to the incandescent, the total light output was much smaller over all.