Diffraction, the Silk Handkerchief, and a Forgotten Founder

Stephen R. Wilk

Between signing the Declaration of Independence, composing opera, and helping to design the U.S. flag, Francis Hopkinson also dabbled in optics—using his silk handkerchief to observe diffraction.



imageForgotten founder Francis Hopkinson

Relatively few of the founding fathers of the United States are familiar to most Americans—which is a shame, since many were fascinating individuals who had accomplishments in several fields. Many have been completely eclipsed by the most famous founders, including George Washington, Thomas Jefferson, Benjamin Franklin, John Adams and a handful of others. (Samuel Adams, who made many contributions to the Revolutionary War, is best known for the beer with his name—although he may not have been a brewer himself.)

Francis Hopkinson is one of the founders who has fallen into obscurity. He was a delegate to the Continental Congress from New Jersey, a signer of the Declaration of Independence, and an accomplished musician who composed the first American opera and a songbook. He was also a poet, a lawyer, and an author of satirical works. Last but not least, Hopkinson was an inventor and scientist and a member of Benjamin Franklin's Philosophical Society of Philadelphia.

Hopkinson was sitting at his front door one evening in 1785 when he decided to perform a little experiment. He stretched his silk handkerchief between his hands and looked at a street lamp about 100 yards away. Out of this diversion came some interesting and important optical physics. Hopkinson expected to see the threads of his handkerchief magnified, and he wasn't disappointed; he reported that the threads appeared to be the size of "very coarse wires."

However, for what followed, he had no explanation. "Although I moved the handkerchief to the right and left before my eyes, the dark bars did not move at all, but remained permanent before the eyeĆ¢€¦ To account for this phenomenon exceeds my skill in optics."

Unable to understand what he had observed, Hopkinson decided to consult an associate who did have the necessary skill—David Rittenhouse, a member of his professional circle. Rittenhouse, like Hopkinson, was a member of the Philosophical Society and a trustee of the University of Philadelphia, which would go on to become the University of Pennsylvania. He was also America's foremost astronomer.

Rittenhouse was a natural modelmaker from an early age, branching out into scientific instruments. He built two orreries—mechanical devices that show the positions and motions of the planets and moons in the solar system—in exchange for which Rutgers University in New Jersey gave him a scholarship. A self-taught astronomer, he constructed his own telescope and made a careful measurement of the transit of Venus on June 3, 1769. In 1781, he observed Uranus. From 1779 to 1782, he was a professor of astronomy at the University of Philadelphia.

Rittenhouse looked into Hopkinson's problem, and he wrote up his results and delivered them to the Philosophical Society almost a year later. "The experiment you mention," he began, "is much more curious than one would at first imagine. For the object we see is not the web of the handkerchief magnified, but something very different..." Rittenhouse recognized the effect as due to what Newton called the inflection of light—a phenomenon that today is called diffraction.

In order to study the effect more precisely, Rittenhouse constructed a model. Instead of using a normal handkerchief with roughly uniform spacing, he asked a watchmaker to put minute threads on pieces of brass wire—106 to the inch—and then he laid down threads between the grooves he had created. Looking at a distant source, he saw four or five colored sets of bars on either side of the central image.

He rebuilt the device with threads that were 1/250 of an inch apart. The colored side bands were brighter and more distinct. He used a measuring device from his telescope to assess the angles that the different colors made, and he noted that the angles that the sets of the same colors he created with the perpendicular to the surface were integral multiples of the angle the innermost one made with the normal.

"I was surprised to find that the red rays are more bent out of their first direction, and the blue rays less; as if the hairs acted with more force on the red than the blue rays, contrary to what happens by refraction," he said. "It is, however, consonant to what Sir Isaac Newton observes with respect to the fringes that border the shadows of hairs and other bodies..."

He went on to state that: "By pursuing these experiments, it is probable that new and interesting discoveries may be made, respecting the properties of this wonderful substance, light, which animates all nature in the eyes of man, and perhaps above all things disposes him to acknowledge the Creator's bounty. But want of leisure obliges me to quit the subject for the present."

Unfortunately, he never found the leisure to take it up again. He was treasurer of Pennsylvania until 1787, and he also served in several offices at the Philosophical Society; he became president in 1791 and director of the United States Mint from 1792 until shortly before his death.

If he'd had the opportunity, he could have pursued his experiments in diffraction and perhaps been the first to measure the wavelengths of the colors of light. Because his pocket handkerchief model was the first consciously constructed diffraction grating, and the several bars of colors at multiple angles was clearly multiple-order diffraction. Thomas D. Cope estimated that Rittenhouse's measurements give about 620 nm for the red light and 460 nm for the blue.

Of course, connecting the measurements with wavelengths requires a philosophical leap to the wave model of light. Whether or not Rittenhouse would have made this leap is now impossible to know. Newton himself, in measuring the sizes of the colored bands associated with what we now call Newton's rings, had associated characteristic lengths with the colors, but he was committed to the corpuscular theory of light, and he did not recognize these as wavelengths.

It is interesting that, although Christiaan Huygens and Robert Hooke had championed the wave theory of light, they did not ask what the wavelength of the light might be—or what its significance was. It remained for Thomas Young, the indefatigable defender of the wave theory, to finally obtain his own grating and to measure, for the first time, the wavelengths of different colors in 1802. Young didn't make his own diffraction grating, as Rittenhouse did. In fact, he didn't need to make anything at all—he used off-the-shelf technology, in the form of finely graven reticules made by a Mr. Coventry of Southwark, England.

There's an interesting postscript to the story. Francis Hopkinson went on to become a member of the Navy Board that wrote the Flag Act of 1777. In later years, he claimed to have designed the U.S. flag. This has been disputed, but Hopkinson definitely had input into the design, which consisted of alternating red and white horizontal stripes and an upper-left canton of white stars in a blue field. These stars were said to have represented the "new constellation" of the United States. They were also rumored to signify the premier American astronomer of the time—David Rittenhouse.

Stephen R. Wilk is an optical engineer with Lincoln Labs in Lexington, Mass., U.S.A.

References and Resourcess

>> "An Optical Problem, Proposed by Mr. Hopkinson, and Solved by Mr. Rittenhouse," Trans. Amer. Phil. Soc. 2, 201-6 (1786).
>> "Second Bakerian Lecture: On the Theory of Light and Colours," Phil. Trans. Royal Soc. London 92, 12-48 (1802).
>> T.D. Cope. "The Rittenhouse Diffraction Grating," J. Franklin Institute 214(1), 99-104 (1932).

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