Everyday Optics

How Retroreflectors Really Work Retroreflectors, wh ich reflect l ight f rom automobile headlamps back in the same direction from wh ich the l ight or igi­nated, are invaluable safety devices. They are entirely passive, requir ing no power supply or maintenance. They make street signs, lane dividers, bicy­clists, joggers, and road crews highly visible. A l though less than 100 years o ld, the devices are now ubiquitous and i n d i s p e n s a b l e . E v e n so, most peop le do not know h o w they work, and those who think they do are probably wrong. Certainly the ex­planation I was given when I began my study of optics (and wh ich I have heard from others as well) was demonstrably incorrect.

There are two types of common retroreflectors—those consisting of ar­rays of corner cubes and those consist­ing of collections of "cat's eyes." 1 The former are probably the most common. They are easily manufactured in bulk out of a variety of plastics, and can be tinted in different colors. Because the cross-section is hexagonal or triangu­lar, it is easy to completely cover the surface of a reflector w i th an array of such constructions (Fig. 1). The pr in­ciple is straightforward and uncompl i ­cated, and w i l l not concern us further.

Corner cubes require a wel l -de­fined and oriented surface, however, and reflective tapes and paint often use a very different method. Glass or plas­tic beads are embedded into the mate­rial. Light that falls upon these beads ends up being reflected pr imar i ly back along its direction of origin. The phe­nomenon is the same one responsible for the "g l ow" from the eyes of animals caught in one's headlights. It is used in "beaded" projection screens, and was once used in a craft called "pastinella work," in which tiny glass spheres were scattered across painting whi le the paint

was sti l l damp. When light came f rom beh ind the v iewer , such pa in t ings seemed to l ight up themselves. The u l ­timate inspirat ion for most of this is the na tura l phenomenon ca l led " h e i l i ­genschein," in wh ich a person standing before a dew-covered f ield w i th the ris­ing sun behind h im sees his shadow surrounded by a bright g low. 2

The usual explanation given for the strongly r e t r o r e f l e c t e d l ight is that l ight fo l lows a path similar to that in the case of a pr i ­

mary rainbow (Fig. 2). The ray is re­flected upon entering the drop, strikes the rear surface, f rom wh ich it suffers Fresnel reflection, then refracts upon str iking the side of the drop again, exit­ing in the direction f rom wh ich it came. There are a number of objections to this route. First, it can be shown that such a path only exists if the index of the drop lies between √2 and 2.0. Water (with an index of 1.33) w i l l not support such a

path, yet the effect is often seen in aque­ous media, such as animal eyes and dewdrops. Second, l ight that is scat­tered f rom a spherical drop after un­dergoing a single internal reflection is

concentrated along the rainbow angle, approximately 138° from the direction of i n c i d e n c e ra ther than b e i n g retroreflected along the direction 180° f rom the direction of incidence. This l ight is, in addit ion, broken up into its constituent spectral colors, whi le the l ight f rom "cat's eys" retroreflectors is

white. Th i rd , even where the index is sufficiently h igh to al low retroreflec­t ion, the result ing rays are restricted to near the edges of the drop. The center of the drop is dark. 3 In retroreflectors, hei l igenschein, and animal eyes, the entire drop lights up uni formly bright.

The "cats eye" effect is thus rather remarkable—it occurs for drops of al l indices and sizes, prov id ing very close to exact retroreflection. The mechanism is somewhat unexpected (Fig. 3). Light f rom some distant source is focused by the drop onto a surface very close to the drop, perhaps even the rear surface of the drop. The focusing is not com­plete, since the surface lies closer than the focal point of the crude lens, but does result in a more constrained circle

S T E P H E N R. WILK is senior optical sys­

tems engineer with Optikos Corp., Cam­

bridge, Mass.

MOST PEOPLE DO NOT KNOW

HOW T H E Y WORK . . .

FIGURE 1. ARRAY OF CORNER CUBE RETROREFLECTORS (AFTER VAN LEAR).

FIGURE 2. PATH OF LIGHT IN THE COMMON EXPLANATION OF RETRORE­FLECTION FROM WATER DROPLETS AND "CAT'S EYES" (AFTER TRICKER). NOTE THAT NO LIGHT IS REFLECTED FROM THE CENTRAL PORTION OF THE SPHERE.

6 OPTICS & PHOTONICS N E W S / D E C E M B E R 1993

of light. Since the light paths are re­versible, the drop also acts to direct light reflected f rom this surface back along its original direction. Put another way, a viewer looking nearly along the direction of the incidence is in precisely the correct location to see the drop act as a magnifier for the spot of light. In his Introduction to Meteorological Optics, Tricker shows very effectively that this is the operating mechanism by use of flasks fi l led wi th water and a white card. If the card is placed very close to the flask, the flask is seen to light up, whi le if the card is moved far away f rom the flask there is no notable retroreflection.

The result is very desirable f rom the point of v iew of manufactur ing— there are no tight tolerances on indices, reflectivities, sizes, or distances. A l l one needs is to suspend glass or plastic spheres in such a way that they become partly uncovered as the paint dries.

It is interesting to note that the na tu ra l re t ro re f lec to r effect of heiligenschein is probably responsible for an almost universal symbol of hol i ­ness—the halo, or aureole. Anyone ob­serving the effect w i th a light source behind them w i l l see the head of their

shadow s u r r o u n d e d by the br igh t retroreflected light. If others are present, each w i l l see the head of his or her shadow surrounded by this burst of i l luminat ion (but they w i l l not see this halo around the shadows of their com­panions.) The Renaissance artist and go ldsmi th (and egotist) Benvenuto Cel l in i was said to have seen in this evidence of his own magnificence. The more prosaic explanation that only one's own head's shadow lies near the posi ­t ion f rom wh ich the incident l ight is retroreflected into the eye is i l lustrated by photographs of the effect taken wi th a tr ipod-mounted camera. Here it is the shadow of the unat tended camera, wh ich is surrounded by a saintly halo. 4

A more epigrammatic cal l to humi l i ty was issued a century ago in the pages of Nature: "Nature naturally takes no

account of moral analogies, of wh ich Nature herself is ful l . Else one might note that a man never sees a halo round his own head unless he turns his back to the l ight." 5

R E F E R E N C E S

1. G . A . V a n Lear , Jr. "Ref lectors used i n h igh ­w a y signs and w a r n i n g s ignals, parts I, II, and III," Journa l of the Op t i ca l Society of A m e r i c a 30, 1940, 462.

2. R .A .R . Tr icker , Introduction to Meteorological Optics, A m e r i c a n E lsev ier Pub l . , N e w Y o r k , N . Y . 1970, 24-42.; M . M innaer t , The Nature of Light and Colour in the Open Air, Dove r P u b l i ­cat ions 350, N e w Y o r k , N . Y . 1954, 230-234.

3. See Plate II, T r icker 6, 37. 4. Ib id. , p. 26. 5. "B .W .S . " Na tu re 38, 1888, 589.

F I G U R E 3 . T R U E L I G H T P A T H IN

" C A T ' S E Y E " T Y P E R E T R O R E F L E C T O R S .

T H E S C A T T E R I N G S U R F A C E M A Y B E

T H E R E A R S U R F A C E O F T H E S P H E R E ,

R A T H E R T H A N A S U R F A C E C L O S E T O

T H E S P H E R E .

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