Thomas B. Greenslade, Jr.
Kenyon College, Gambier, Ohio 43022 USA
Photometers are used to compare the intensity of one light source to another. If you know something about the properties of the standard light source, you now have a number that you can use to study illumination. The Photometers discussed in this paper depend on the perceived overall reaction of the human eye, which has a sensitivity that is both wavelength and intensity dependent.
Standard Sources of Light
The response curve of the human eye is roughly bell-shaped, with the peak at about 500 nm under low light conditions, and about 10% higher for daylight conditions. The choice of a standard source of light for illumination studies thus depends on both its overall intensity and its spectral content.
Historically, standard sources have been incandescent: either glowing soot (from a candle or other flame-producing source) or the glowing filament of an incandescent light bulb. By their nature these sources are arbitrary, although they have been designed to be reproducible. The English standard candle, first suggested by Count Rumford (Benjamin Thompson, 1753-1814), was made of spermaceti, a wax obtained from sperm whale oil, consumed at a rate of 7.776 grams per hour with a flame height of 4.5 cm. The diameter of the candle was 2.22 cm. Figure 1 shows a late 19th century standard light source. The 1916 catalogue of the L. E. Knott Apparatus Company of Boston lists this as the “Hefner Lamp, approved by the Physikalish-Technischen Reichsanstalt as the German Photometric Standard Source of Light, burning amyl-acetate [banana oil].” Its duty-free price was $12.50; with a certificate of calibration the price was $16.50.
The Inverse-Square Law
Many photometers depend on the application of the inverse-square law. The idea is straight-forward: energy from a point source is carried outward in a uniform three-dimensional medium in the form of a sphere. The information is spread evenly over the surface of the sphere, and the energy density is spread more thinly over the surface as the sphere expands. Since the area of the sphere is proportional to the square of its radius R, the energy density decreases as 1/R2. Figure 2 is a diagram showing the relationship between distance and surface area, this time on small segments of spheres that can be approximated as planes.
The Swiss-German scientist and mathematician, Johann Heinrich Lambert (1728-1777) was one of the first to devise a photometer to measure relative intensities of light, and the Lambert, a measure of light intensity is named after him. By the early part of the 20th century, his 1760 design, now named after Count Rumford who had used it in his research, took the form shown in Figure 3. The 1916 catalogue of the L.E. Knott Apparatus Co. of Boston notes that “This Photometer consists of a wooden base board upon which are mounted two converging meter sticks. At the point of convergence is mounted a blackened rod, designed to cast a shadow on the opaque screen held in the vertical support [on the] left-hand side. … The sources of illumination are mounted on a base board, one on their side of the light shield…$3.50”. Other forms of Rumford’s photometer are given in Reference 1.
If one of the two light bulbs is turned off, the single shadow on the screen will be truly black. Turning on the other bulb illuminates this shadow, and produces a second partly illuminated shadow. The two light bulbs are then moved back and forth until the two shadows have the same intensity, and the inverse square law is applied: the intensity of the unknown at a distance x from the screen is related to the intensity I(0) of the standard source a distance s from the surfaces by
I = I(0) (x/s)².
Bunsen’s Grease-Spot Photometer
The grease-spot photometer, once a common experiment in high school physics courses, was invented by the prolific German scientist Robert Bunsen (1811-1899). The key element is a sheet of white paper with a translucent grease spot a couple of centimeters in diameter. The translucent section will appear darker by reflected light (its reflectivity is less than the rest of the paper) and lighter by transmitted light. This is illuminated from one side by the standard light source and from the other by the unknown, and the distances between the sources and the paper adjusted until the grease spot disappears. Under these conditions the light reflected on one side from the surface of the spot is just compensated by the light transmitted from the other side – this condition can only be met when the illumination is equal on both sides. Once more, the inverse square law is used to find the intensity of the unknown source in terms of the intensity of the standard.
Figure 4(a) shows a Bunsen photometer made by the Central Scientific Company that is in the author’s collection. Figure 4(b) is a cut from the 1940 catalogue. The known and unknown sources (in this case a standard candle and a lamp) are placed at the ends of the 120 cm long case; the chimneys allow heat to escape while baffling light. The grease spot is in the middle of the sliding apparatus in the central section, and mirrors angled behind it allow both sides to be observed at the same time.
The Bunsen grease spot principle is used in the Foot Candle Meter in Figure 5. At one time light bulbs were rated in foot-candles, and it should be no surprise that this meter was made by the Engineering Department of the National Lamp Works of the General Electric Co., Nela Park, Cleveland, Ohio. Inside the case a rubber stamped notation that cancels a “Patent Applied For” note and replaces it with “Patented March 31, 1919.”
Underneath the hinged cover is a series of identical small disks of translucent paper. These are illuminated from below by a small lamp at the left-hand end, and the illumination of the disks from below falls off according to the inverse square law. The light bulb is powered by a battery in series with the rheostat on the light-hand side; this is used for standardization. The candle power rating of the lamp under test is determined when a particular disk appears to be equally illuminated by the internal bulb and the test lamp.
This device is described in the 1922 catalogue of the W. M. Welch Scientific Company of Chicago. No price is given, but the 1929 catalogue of the Chicago Apparatus Company lists it at $35.00. This example is in the Greenslade Collection.
The Lummer-Brodhun Photometer
The photometer in Figure 6, now in the Greenslade collection, is of the Lummer and Brodhun style, and was sold by Leeds & Northrup. Otto Lummer and Eugen Brodhun of the Physikalish-Technische-Reichanstalt in Berlin developed the instrument in 1889. In this design, the user looks through the eyepiece and, due to internal beam-splitters and
mirrors, is able to see both sides of an illuminated disk at the same time and thus compare their relative brightness. Adjustments are made in the distances of the unknown and the standard to the instrument and the inverse square law is employed. The page from the 1919 L&N catalogue shows the optical system. A spare matte-white disk is shown on the right-hand side. Photometers of this type are still in use today. This instrument cost $90 in 1919.
Charles Wheatstone (1802-1875) has long been one of my favorite Victorian physicists, despite the fact that he did not invent the “Wheatstone” bridge. He is, however, responsible for the form of photometer shown in Figure 7 (Ref. 1). Here he was concerned with producing bright spots, from the two light sources, that can easily be compared. If you look
closely at the steel bead in the figure, you can see images of the two 150 W light bulbs that were used to illuminate the instrument when it sat for its portrait. These are real images of the lights, greatly reduced in size, as you might expect from a convex mirror. The geared mechanism of the photometer is used to move the bead rapidly in a highly-eccentric ellipse, and the persistence of vision makes two images appear to trace out parallel ellipses. It is then easy to move the two light sources until the ellipses have equal brightness, and the usual inverse-square calculation can be made. It is probable that this instrument was suggested by Wheatstone’s Kaleidophone (Ref 2) in which the image of a bright light source produced by a bead mounted on the end of a vibrating rod appears to trace out complex figures. And, in this form, Wheatstone’s photometer may be used once more: simply wax a shiny bead onto the end of a piece of springy wire that is held upright in a vise, place it between the two unknown light sources and set the bead vibrating.
The surface temperature of a body heated to incandescence is related directly to the peak wavelength of the visible radiation given off by the body. The optical pyrometer in Figure 8 allows the remote sensing of the temperature of a black body in the 1400° F to 3400° F range. The body may be a stream of molten copper or silver, a pot of molten steel or the hot bed of coals under a steam boiler. Inside the tube is a lamp whose temperature is controlled by a rheostat and a battery in the box slung by a strap around the user’s neck. The tube (part of a stereoscopic hand viewer that was common at the time) is pointed toward the hot body, and the image of the filament is superimposed on the image of the hot body.
The temperature of the filament is adjusted until it can no longer be seen against the image of the body under test. The instrument was made by Leeds & Northup in 1930, and cost $175. It is in the Greenslade Collection.
The Photo-Electric Light Meter
The modern instrument has been saved for last. A photovoltaic cell, first made commercially available by the Weston Electric company about 1925, puts out a voltage signal that depends on the intensity of the light. One of the first applications was to room illumination and Figure 9 shows the Weston Photronic Foot-Candle Meter that is listed at $19.50 in the 1937 Central Scientific catalogue. For this purpose the scale is divided into regions related to vision: “Inadequate for critical seeing”, “Reading usual print”, etc. The text suggests that it could also be used as a laboratory test of the inverse square law, and for this purpose there is a non-linear scale running from 0 to 75 foot-candles.
Hand-held photographic light meters are now passing out of general use, but they can be used in the laboratory for photometric measurements. The author has described the use of such a meter in measuring the exponential reduction in the intensity of light as a series of identical neutral density filters is placed between the meter and a light source. (Ref. 3)
- Thomas B. Greenslade, Jr., “Nineteenth Century Textbook Illustrations XII: Two Photometers”, Phys. Teach., 15 (1977), 44-45.
- Thomas B. Greenslade, Jr., Nineteenth Century Textbook Illustrations LI: The Kaleidophone”, Phys. Teach., 30 (1992), 38-39.
- Thomas B. Greenslade, Jr., “An Inexpensive Optical Absorption Experiment”, Phys. Teach., 44 (2006), 348-350.