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.

 

Section 36–3 The rod cells

(Plane structures / Chemical bond / Light absorption)

 

In this section, Feynman discusses plane structures, chemical bond, and light absorption of retinal in rod cells. Thus, the section could be titled as “the retinal of  rhodopsin (or photoreceptor cells).”

 

1. Plane structures:

“The rhodopsin, which is the pigment, is a big protein which contains a special group called retinene, which can be taken off the protein, and which is, undoubtedly, the main cause of the absorption of light (Feynman et al., 1963, p. 36–6).”

 

In his Nobel lecture, Wald (1968) mentions: “… Ball, Goodwin and Morton in Liverpool showed that retinene is vitamin A aldehyde. At Morton’s suggestion the names of all these molecules have recently been changed, in honor of the retina, still the only place where their function is understood. Vitamin A is now retinol, retinene is retinal; there is also retinoic acid.” That is, the term retinene is outdated and had been replaced by retinal, which is more commonly used in current literature. Retinal also refers to the aldehyde form of Vitamin A, which is an essential component of rhodopsin and plays a crucial role in visual phototransduction. Visual phototransduction is the photochemical reaction where light is converted to an electrical signal in the retina.

 

“There are layer after layer of plane structures, shown magnified at the right, which contain the substance rhodopsin (visual purple), the dye, or pigment, which produces the effects of vision in the rods (Feynman et al., 1963, p. 36–6).”

 

Feynman says there are layers of plane structures, which contain the rhodopsin molecules and adds that there is some reason for holding all the rhodopsin molecules parallel. Specifically, rod cells contain a light-sensitive pigment called rhodopsin, which consists of a protein called opsin and a light-absorbing molecule called retinal. However, the retinal molecule within rhodopsin is non-planar. In Wald’s (1968) words, “A cis-linkage always represents a bend in the chain; but because of this steric hindrance the 11-cis molecule is not only bent but twisted at the cis linkage. This departure from planarity, by interfering with resonance, was expected to make the molecule so unstable that one hardly expected to find it.” That is, the non-planarity is essential for the molecule’s light-absorption properties and the structural changes upon absorbing light.

 

2. Chemical bond:

“This kind of a structure, with layers, appears in other circumstances where light is important, for example in the chloroplast in plants, where the light causes photosynthesis. If we magnify those, we find the same thing with almost the same kind of layers, but there we have chlorophyll, of course, instead of retinene. The chemical form of retinene is shown in Fig. 36–6. It has a series of alternate double bonds along the side chain… (Feynman et al., 1963, p. 36–6).”

 

Feynman explains that retinene has a series of alternate double bonds in the side chain. The term “alternate double bonds” refers to a sequence of double bonds that is separated by single bonds (-C=C-C=C-). Double bond is a chemical bond between two atoms involving two pairs of electrons instead of a pair of electrons in a single bond. He also uses the term “conjugated double bonds,” which is extended to the analogous interaction involving a p-orbital containing an unshared electron pair (IUPAC, 2014). It means that the electrons can move freely across alternate double bonds allowing for delocalization of electrons in the retinal. While both terms describe the arrangement of double bonds in retinal, conjugated double bond emphasizes the electronic delocalization and unique optical properties of the molecule.

 

This substance is impossible for human beings to manufacture in their own cells—we have to eat it. So we eat it in the form of a special substance, which is exactly the same as retinene except that there is a hydrogen tied on the right end; it is called vitamin A, and if we do not eat enough of it, we do not get a supply of retinene, and the eye becomes what we call night blind, because there is then not enough pigment in the rhodopsin to see with the rods at night (Feynman et al., 1963, p. 36–6).”

 

Eating retinol (vitamin A) or beta-carotene (provitamin A) is crucial for preventing night blindness because these compounds are essential for the production of retinal, a key component of rhodopsin (Grune et al., 2010). Rhodopsin is responsible for vision in low-light conditions, such as those encountered during nighttime. Retinol and beta-carotene are precursors of retinal: Retinol can be directly converted into retinal in the body, while beta-carotene is converted into retinol and then retinal through metabolic processes. Thus, consuming foods rich in retinol (such as liver, fish and dairy) or beta-carotene (plant-based foods such as carrots, spinach, and lettuce) ensures that the body has a supply of retinal for the production of rhodopsin. However, it is incorrect for Feynman to say that human cannot manufacture retinene (or retinal) because they can convert beta-carotene into retinol and then retinal.

 

3. Light absorption:

“When light strikes this molecule, the electron of each double bond is shifted over by one step. All the electrons in the whole chain shift, like a string of dominoes falling over, and though each one moves only a little distance (we would expect that, in a single atom, we could move the electron only a little distance), the net effect is the same as though the one at the end was moved over to the other end! It is the same as though one electron went the whole distance back and forth, and so, in this manner, we get a much stronger absorption under the influence of the electric field, than if we could only move the electron a distance which is associated with one atom (Feynman et al., 1963, p. 36–6).”

 

Retinal is a conjugated chromophore (a molecule which absorbs light at a particular wavelength and emits color subsequently) that is responsible for our ability to see. When light strikes rhodopsin, retinal undergoes a transformation from its 11-cis form (rhodopsin) to its all-trans form (metarhodopsin), initiating a cascade of biochemical events that result in the generation of electrical signals in the rod cell, enabling vision in low-light conditions. The key to the absorption of light by retinal lies in the conjugated double bonds that are essential for the molecule’s light-absorbing properties. However, electrons do not move in a coordinated manner along a chain of atoms as dominoes do. The behavior of electrons in a conjugated system is more complex and involves delocalization, where electrons are spread out over the entire molecule.  

 

In its native form within visual pigments, retinal exists in the 11-cis configuration and all-trans configuration. The 11-cis prefix is due to the double bond at the 11^th carbon atom is connected to the two largest substituents whereby the largest chains are on the same side. The all-trans prefix (trans is a Latin prefix meaning across or on the other side) refers to the double bonds with the bulky substituents (e.g., hydrogens) are positioned on opposite sides. When light enters the eye and strikes the retina, it breaks the C=C double bond between C₁₁ and C₁₂ atom and causes a rotation to form the all-trans configuration (as shown below). After the change, the all-trans-retinal is later converted back into 11-cis-retinal through a series of enzymatic reactions and allowing the visual pigment for further light absorption.

Source: Das et al., 2024.

 

Review Questions:

1. Is the retinal molecule within rhodopsin planar or non-planar?

2. How would you explain the chemical bond of retinene (retinal)?

3. How would you explain the absorption of light by retinal?

 

The moral of the lesson: retinal molecule within rhodopsin has a non-planar structure and conjugated double bonds where electrons can move across the alternating single and double bonds, and thus, play a crucial role in light absorption.

 

References:

1. Das, U., Das, A., Das, R., & Das, A. K. (2024). Photochemistry of the retinal chromophore in the process of seeing (vision). ChemTexts, 10(2), 3.

2. Grune, T., Lietz, G., Palou, A., Ross, A. C., Stahl, W., Tang, G., ... & Biesalski, H. K. (2010). β-Carotene is an important vitamin A source for humans. The Journal of nutrition, 140(12), 2268S-2285S.

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. IUPAC (2014). Compendium of chemical terminology. Compiled by A. D. McNaught & A. Wilkinson. Oxford: Blackwell Scientific Publications. Retrieved October 8, 2014 from http://goldbook.iupac.org/.

5. Wald, G. (1968). Molecular basis of visual excitation. Science, 162(3850), 230-239.

Section 36–2 The physiology of the eye

(Underwater vision / Binocular vision / Inverted vision)

 

In this section, Feynman discusses neural machinery, optical components, and neural connections of human eyes. However, the discussions could be related to underwater vision, binocular vision, and inverted vision.

 

1. Underwater vision:

“This is why we cannot see clearly under water, because we then do not have enough difference between the index of the cornea, which is 1.37, and that of the water, which is 1.33. Behind the cornea is water, practically, with an index of 1.33, and behind that is a lens which has a very interesting structure: it is a series of layers, like an onion, except that it is all transparent, and it has an index of 1.40 in the middle and 1.38 at the outside (Feynman et al., 1963, p. 36–3).”

 

Feynman explains that we cannot see clearly under water because the difference between the refractive index of the cornea and water is not enough. One may clarify the ability of cornea, humor, and lens of the human eye to focus images (bend light rays) on the retina, but the clarity of the images is dependent on the ratio of refractive index of the cornea and that of the medium where the object resides. Based on research data over the recent 20 years, the refractive index of cornea changes from about 1.400 at the epithelium to 1.373 at the endothelium (Patel & Tutchenko, 2019). However, the unclear underwater vision is also due to the light absorption in water whereby the attenuation is dependent on the wavelength of light. Furthermore, the absorption and attenuation are dependent on the depth and turbidity of the water.

 

It should be worth mentioning that the human eye is adapted for viewing in air because the ratio of the refractive index of cornea to that of the air (Snell’s law of refraction) is relatively larger. On the other hand, fishes have a better underwater vision because their corneas are more spherical and thus, they can bend light rays better to achieve a better focus. A disadvantage of fishes’ corneas is that it causes them to be short-sighted when viewing in air. Interestingly, penguins are able to focus more clearly on land and underwater, but their corneas are relatively flatter than other birds (Hadden & Zhang, 2023). Essentially, the penguins’ lenses are softer and their eye muscles can adjust the shape of the lens more than other animals to view in air and underwater.

 

2. Binocular vision:

“This is the manner in which the information from each of the two eyes is put together in order to tell how far away things are. This is the system of binocular vision (Feynman et al., 1963, p. 36–4).”

 

Binocular vision is the integration of monocular sensory and motor visual information into a combined percept of the surrounding physical space (Stidwill & Fletcher, 2017). There are at least three conditions for binocular vision: (1) Interocular distance: Two eyes and a separation between the eyes (interocular distance), which is about 65 mm in adult humans. (2) Neural pathway: A neural pathway (or neural connections) to transfer the two images to the brain. (3) Neural machinery: Neural processing systems to integrate the different types of visual information, such as luminosity, size, color and contrast. According to Feynman, the binocular vision tells how far away things are, but one may add that it is the ability of human eyes to perceive a three-dimensional image by combining the two images from the left and right eyes simultaneously.

 

“… it is impossible consciously or unconsciously to turn both eyes out at the same time, not because there are no muscles, but because there is no way to send a signal to turn both eyes out, unless we have had an accident or there is something the matter, for instance if a nerve has been cut. Although the muscles of one eye can certainly steer that eye about, not even a Yogi is able to move both eyes out freely under voluntary control, because there does not seem to be any way to do it (Feynman et al., 1963, p. 36–5).”

 

There are two aspects of binocular vision, convergent vision and divergent vision, which is the ability of both eyes to move together to perceive depth and distance. In general, vergence eye movements consist of simultaneous movement of both eyes in opposite directions that maintain binocular vision. Convergent vision (or convergence eye movement) occurs when both eyes focus on a nearby object, i.e., the eyes rotate inward, towards each other, to align their lines of sight onto the object. On the contrary, divergent vision (or divergence eye movement) occurs when both eyes focus on a distant object, whereby the eyes rotate outward, away from each other, to align their lines of sight onto the object. Interestingly, a person (non-Yoji) may have partial divergence eye movement, e.g., right eye diverging while left eye remains relatively stable as shown below.

 

Source: Vergence - Wikipedia

3. Inverted vision:

“Believe it or not, the up-and-down line in our visual field as we look at something is of such a nature that the information from all the points on the right side of that line is going into the left side of the brain, and information from the points on the left side is going into the right side of the brain, and the way this area is made, there is a cut right down through the middle, so that the things that are very close together right in the middle are very far apart in the brain! (Feynman et al., 1963, p. 36–4).”

 

One may adopt the term inverted vision (or left-right reversed vision) that refers to a vision related to the interpretations of the eye-brain system. In short, the inverted image formed on the retina of the eye is “re-inverted” by the brain. In other words, the visual information is processed and inverted by the brain to present a coherent and upright perception of the world observed by the eyes. On the contrary, a lady by the name of Marietta Everett had up-down inverted vision and see the world upside down (Davis, 1969). Due to the image is inverted on the retina and abnormalities in the visual cortex, the brain would receive a reversed representation of the visual scene. While most people perceive the world upright through perceptual adaptation, Everett’s brain was unable to perform this adaptation, resulting in her perception of the world as inverted.

“This is an important point, because most of the earlier books on anatomy and psychology, and so on, do not appreciate or do not emphasize the fact that we are so completely wired already—they say that everything is just learned (Feynman et al., 1963, p. 36–6).”

 

Perceptual adaptation refers to the brain’s ability to adapt to distorted sensory inputs over time, allowing individuals to perceive these inputs as normal or familiar. In Erismann and Kohler’s Innsbruck Goggle experiments, perceptual adaptation is demonstrated through the subjects’ ability to adapt to wearing upside down goggles (e.g., flipping top and bottom or flipping left and right). Despite initially perceiving a distorted world through the goggles, over time the subjects were able to interpret the transposed visual information as normal. In other words, the perceptual experience of the reversed image may become normalized, and individuals may perceive it as if it were in its original orientation. The orientation of visual information in the brain is determined by the arrangement of neural connections from the eyes to the visual cortex.

 

Review Questions:

1. How would you explain underwater vision?

2. How would you explain binocular vision?

3. How would you explain inverted vision?

 

The moral of the lesson: Underwater vision, binocular vision, and inverted vision are related to refractive index, eye movements (or ocular motility), and perceptual adaptation.

 

References:

1. Davis, B. (1969). Upside-down girl baffles scientist, Jet, 36(26), 17-22.

2. 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.

3. Hadden, P. W., & Zhang, J. (2023). An overview of the penguin visual system. Vision, 7(1), 6.

4. Patel, S., & Tutchenko, L. (2019). The refractive index of the human cornea: A review. Contact Lens and Anterior Eye, 42(5), 575-580.

5. Stidwill, D., & Fletcher, R. (2017). Normal binocular vision: Theory, investigation and practical aspects. John Wiley & Sons.