Section 36–4 The compound (insect) eye

(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, λ_ave = (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.