How Do We See in the Visible Spectrum?

Light Attenuation

• Definition: Light attenuation refers to the absorption of certain frequencies of sunlight by water. As light traverses through water, both low and high frequencies are absorbed.

• Evolutionary Adaptation: Fish have evolved specialized light-absorbing pigments in their eyes to help them navigate through varying depths and environments in aquatic settings.

Role of Retinal Molecule

• Function: Retinal binds to opsin proteins located in the photoreceptor cells of the eye and is essential for vision in animals.

• Key Question: How does retinal absorb light? The process of absorption causes transitions between distinct energy levels within molecules.

Energy Levels Overview

• Energy Transitions: When an electron transitions from the 3rd to the 2nd excited state, it releases energy in the form of a photon. Conversely, when a photon is absorbed by a molecule, this energy facilitates the electron's jump to a higher energy state.

Absorption and Emission Phenomena

• Energy Level Determination: An accurate understanding of energy levels requires the principles of quantum mechanics. A simplified framework often used is the Standing Wave Model.

• Wave-Particle Duality: Experiments conducted with photons, such as the double slit experiment, illustrate interference patterns. Electrons exhibit analogous behavior, reinforcing the concept of wave-particle duality, which permits treatment of both photons and electrons as waves in specific contexts.

Standing Waves and Molecular Length

• Standing Wave Model in Retinal: Within the context of the retinal molecule, electrons behave as standing waves, which are confined by the length of the retinal molecule (denoted as L).

• Tasks for Analysis:

  1. Draw the 3rd and 4th standing waves for electrons confined in a molecule of length L.

  2. Write general expressions to find the wavelength of the nth standing wave as a function of L.

  3. Estimate the length (L) of the retinal molecule using standard bond lengths:

     • Single bond length ~0.154 nm

     • Double bond length ~0.134 nm

Valence Electrons in Retinal

• Composition: Retinal consists of 6 double bonds, contributing a total of 12 valence electrons associated with the standing wave model.

• Energy Levels Diagram:

  • Highest occupied level = 6

  • First unoccupied level = 7

Energy Considerations in Electrons

• Energy Difference in Electrons: This can be calculated using the formula for kinetic energy: E = 1/2 me v², which is relevant to the study of standing waves and photon absorption.

• Kinetic Energy: Defined as the energy an object possesses due to its motion; in scenarios where other forces are negligible, only kinetic energy is considered.

Predictions and Findings

• Calculate Energies: Utilize the derived equations and estimated values to determine energies of both occupied and unoccupied energy levels.

• Energy Differences: This provides insight into the energy of the photons that retinal can absorb and the corresponding wavelengths associated with these energies.

• Wavelength in Electromagnetic Spectrum: The energy of a photon is related to its wavelength via the equations (E = hf; c = fλ).

Absorption and Implications

• Absorption and Frequency Ranges: The absorption process leads to specific frequencies lying within particular ranges in the electromagnetic spectrum.

Model Accuracy and Implications for Fish Navigation

• Conclusion on Model Accuracy: The absorption spectrum predicted by the model does not align accurately with empirical data regarding retinal absorption.

• Effects of Size on Light Absorption:

  • If the light-absorbing molecules were ten times smaller, the increased energy gap would shift absorption to higher energies, potentially saturating near water's absorption bands.

  • Conversely, if they were ten times larger, the decreased energy gap would shift absorption towards infrared, thus becoming less efficacious for underwater navigation.

• Optimal Molecular Size: The size of retinal molecules is optimal for fish navigation through variable underwater light conditions, contributing to their ability to thrive in diverse aquatic environments.