(Color vision / Polarization vision / Angular resolution)
In this section, Feynman discusses the color vision, polarization vision, and angular resolution of the compound eye of bees. Alternatively, the
section could be titled as “the compound eye of bees.”
1. Color vision:
“In this way it was discovered that the bee’s eye is
sensitive over a wider range of the spectrum than is our own. Our eye works from 7000 angstroms
to 4000 angstroms, from red to violet, but the bee’s can see down to 3000 angstroms
into the ultraviolet!... It has been shown, however, that there are a few
red flowers which do not reflect in the blue or in the
ultraviolet, and would, therefore, appear black to the bee! (Feynman et al., 1963, p. 36–7).”
According to
Feynman, there are a few red flowers which do not reflect
blue or ultraviolet, and would appear black to the bee! To be
precise, bees can see from approximately 300 nm to 650 nm because they have
three photoreceptors that are maximally sensitive to ultraviolet, blue, and
green light (Hempel de Ibarra et al., 2014). Although it is commonly reported that bees cannot
see red, but bees are seen visiting some red flowers (as shown below). For example, there are some plants pollinated by bees that produce red
flowers such as Onosma confertum (Chen et
al., 2020). In short, the color-deficient bees would perceive other
colors instead of red, and thus red flowers do not necessarily appear black to
the bees. However, bees can be attracted to flowers because of their scent.
Source: Can Bees See Red Flowers? Do Bees Visit Red Flowers? (buzzaboutbees.net)
Bee’s inability to see red color is commonly attributed to Karl von Frisch who was awarded the Nobel Prize for discoveries related to “bee dance.” In Frisch’s experiments, bees were trained to associate colored cards (e.g., red) with a dish of sugar water. Importantly, the word ‘red’ has been defined based on human perception, i.e., the perceptual result of light incident upon the human retina in the visible region of the spectrum, having wavelengths in the region of 400 nm to 700 nm. On the other hand, we should not expect bees to have the same perception of red flowers, but it depends on the light spectra reflected by the so-called red flowers. Perhaps the red cards used in Frisch’s experiments appear to be almost black or dull color, but it should be different from the red flowers.
2. Polarization
vision:
“The
bee can tell, because the bee is quite sensitive to the polarization of
light, and the scattered light of the sky is polarized. There is still
some debate about how this sensitivity operates. Whether it is because the
reflections of the light are different in different circumstances, or the bee’s
eye is directly sensitive, is not yet known (Feynman et al., 1963, p. 36–7).”
Feynman explains that the bee is quite sensitive to
the polarization of light and the scattered light of the sky
is polarized. This could be attributed to Frisch’s research on how bees
use the sun as a compass. If the sunlight is blocked by a cloud, the bees can
make use of the polarized light scattered by the Earth’s atmosphere. Essentially,
bees have polarization vision that is related to the Rayleigh scattering phenomenon,
which occurs when sunlight interacts with molecules in the sky (or Earth’s
atmosphere). Rayleigh scattering is responsible for the blue color of the sky
and contributes to the polarization of scattered light. However, the bees’
flight can be related to the polarization pattern of the blue sky and the
magnet field of the Earth (Von Frisch, 1974).
Feynman says that it is not yet known whether the bee is directly sensitive to the polarization of
light. In another study, a simple “maze” of four tunnels arranged in a cross (with
sugar reward at its end) was used to show that bees are able to follow
polarized light (Evangelista et al., 2014). When the light was
transversely polarized in the “correct” tunnels, bees tended to dance
vertically (or perpendicular) with waggles in the same perpendicular direction to
the tunnels. When the light was polarized parallel to the tunnels, bees tended
to dance horizontally with waggles either to the left or right. This
experiment is more conclusive on the polarization vision of the bees.
3.
Angular resolution:
“The
book says the diameter is 30 μm, so that is rather good agreement!
So, apparently, it really works, and we can understand what determines the size
of the bee’s eye! It is also easy to put the above number back in and find out
how good the bee’s eye actually is in angular resolution; it is very
poor relative to our own (Feynman et
al., 1963, p. 36–8).”
Feynman’s estimation of angular resolution of the bee’s eye could be improved by at
least three ways. Firstly, we may include the factor 1.22 (Abbe's sine condition), which is
due to the diffraction-limits of the eye. Secondly, the size of the bee’s eye
could be specified as r = 1.22 mm based on measurements (Varela & Wiitanen, 1970), but Feynman guesses that r = 3 mm. Thirdly, bees can see
light that vary from about 300 to 650 nm, and thus, one may guess another
wavelength instead
of 400 nm (suggested by
Feynman*). Using r = 1.22 mm, λave = (300 + 650)/2 = 475 nm » 500 nm, and δ=√(1.22λr), we can obtain δ = 27.3 mm, but it is different from
Feynman’s estimate that δ = 35 μm. However, this may suggest a refinement of the mathematical model or
a change of the wavelength used for the model.
In the Audio Recordings* [37 min: 00 sec] of this lecture,
Feynman initially guessed λ = 500 nm and estimated δ = 40 μm, but
later explained that λ could be shorter.
The Feynman Lectures Audio Collection: https://www.feynmanlectures.caltech.edu/flptapes.html
“The
book says the diameter is 30 μm, so that is rather good agreement!
So, apparently, it really works, and we can understand what determines the size
of the bee’s eye! (Feynman et al., 1963, p. 36–8).”
According to Feynman, the book says the diameter is 30 μm and thus, the percentage error is about
(35 – 30)/30 » 17%. Perhaps some may not conclude that it is a rather
good agreement with the book. If we compare the estimated value with an
observed value of δ = 32 μm (Varela & Wiitanen,
1970), the percentage error would be (35 – 32)/32 » 9% and this is a better agreement with the
observed value. However, Feynman might guess different values of λ and r
if he knew a different value of observed δ (e.g., 32 μm) by working backward. The
method of estimation could be refined if we take into account of the
maximal sensitivity of three photoreceptors of the bee’s eye at their peak
wavelength (S-344 nm, M-436 nm, L-556 nm).
Review
Questions:
1.
Do red flowers appear black to the
bees?
2. How would you explain the polarization vision of bees?
3. How
would you determine the angular resolution of the bee’s eye?
The
moral of the lesson: Bees have complex visual systems that include: (1) Color vision
(three photoreceptors sensitive to UV, blue, and green light), (2) Polarization
vision (e.g., navigate using scattered light in blue sky), and (3) Angular
resolution (optimized through evolution to balance acuity and diffraction
limits).
References:
1. Chen, Z., Liu, C. Q., Sun, H., & Niu, Y. (2020). The ultraviolet
colour component enhances the attractiveness of red flowers of a bee-pollinated
plant. Journal of Plant Ecology, 13(3), 354-360.
2
Evangelista, C., Kraft, P., Dacke, M., Labhart, T., & Srinivasan, M. V.
(2014). Honeybee navigation: critically examining the role of the polarization
compass. Philosophical Transactions of the Royal Society B: Biological
Sciences, 369(1636), 20130037.
3. Feynman, R. P., Leighton, R. B., &
Sands, M. (1963). The Feynman
Lectures on Physics, Vol I: Mainly mechanics, radiation, and heat. Reading,
MA: Addison-Wesley.
4. Hempel de Ibarra, N., Vorobyev, M., &
Menzel, R. (2014). Mechanisms, functions and ecology of colour vision in the
honeybee. Journal of Comparative Physiology A, 200,
411-433.
5. Varela, F.
G., & Wiitanen, W. (1970). The optics of the compound eye of the honeybee
(Apis mellifera). The Journal of general physiology, 55(3),
336-358.
6. Von Frisch, K. (1974). Decoding the language
of the bee. Science, 185(4152), 663-668.
