# The Physics of Fogbows

Source: https://www.youtube.com/watch?v=OEQeSrXy-YA
Recap page: https://rapidrecap.app/video/OEQeSrXy-YA
Generated: 2025-10-24T19:02:38.3+00:00

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## Quick Overview

Fogbows, or white rainbows, are created by sunlight interacting with tiny water droplets in fog or mist, which are about 100 times smaller than typical raindrops, resulting in a pale, mostly white arc due to the strong diffraction effects caused by the small droplet size, which spreads out the color spectrum beyond visibility.

**Key Points:**
- Fogbows are optical phenomena similar to rainbows but formed by sunlight interacting with very small water droplets (fog or mist) instead of larger raindrops.
- The small size of fog droplets (around 10 micrometers or less, compared to raindrops at 100 micrometers or more) causes significant light diffraction, which washes out the distinct color separation seen in regular rainbows.
- Regular rainbows exhibit color separation due to refraction and internal reflection at angles around 40{o} (violet) to 42{o} (red), whereas fogbows are seen at an angle of approximately 140{o} (or 40{o} away from the anti-solar point, depending on the definition used for the reflection angle).
- Diffraction causes the spectral colors from fogbows to overlap significantly, resulting in a faint, often white or pale arc, sometimes called a white rainbow.
- The extent of color spreading due to diffraction is inversely proportional to the size of the obstacle (or droplet), meaning smaller droplets lead to a wider, less distinct diffraction pattern (0: $\theta \sim 1/d$).
- Supernumerary bows, which are extra faint, concentric rings inside the primary bow, are caused by the constructive and destructive interference of light waves, a phenomenon that becomes more pronounced and visible with smaller water droplets.

![Screenshot at 0:12: The video introduces the term 'fogbows' over an image of a pale arc in a foggy field, establishing the central topic of the physics explanation.](https://ss.rapidrecap.app/screens/OEQeSrXy-YA/00-00-12.png)

**Context:** This video explains the physics behind fogbows, which are atmospheric optical phenomena that appear as faint, often white arcs in fog or mist, contrasting them with the familiar, vividly colored primary rainbows seen in rain. The core difference lies in the size of the water particles involved: raindrops for rainbows and much smaller water droplets for fogbows. The explanation relies on principles of refraction, reflection, and crucially, diffraction and interference.

## Detailed Analysis

The video explains that fogbows are essentially rainbows formed under different conditions: sunlight interacting with tiny water droplets in fog or mist rather than large raindrops. A key distinction is the size of these droplets; fog droplets are typically around 10 micrometers or less, while raindrops are 100 micrometers or larger. This size difference dictates the physics observed. For regular rainbows, light refracts and reflects inside the spherical raindrops, separating colors (dispersion) into distinct bands visible between 40{o} and 42{o} from the anti-solar point. In contrast, the much smaller fog droplets cause significant diffraction, where light waves spread out after passing near or reflecting off the droplet. Since diffraction spreading ($\theta \sim 1/d$) is inversely proportional to the size ($d$) of the obstacle, the colors spread out so much that they overlap, causing the visible spectrum to blur into a pale or white arc, hence the term 'white rainbow.' The video illustrates this by comparing the sharp color bands of a large-droplet rainbow simulation with the broad, overlapping rings of a small-droplet simulation, which produces the ghost-like fogbow appearance. Furthermore, the diffraction mechanism creates supernumerary bows—concentric rings inside the main arc—which are far more pronounced in fogbows than in regular rainbows where they are often too faint to see.

### Fogbow vs. Rainbow Formation

- Fogbows form in fog/mist via sunlight interacting with tiny water droplets (d < 10 $\mu$m)
- Rainbows form in rain via sunlight interacting with larger raindrops (d > 100 $\mu$m)
- Both involve refraction and reflection, but fogbows are dominated by diffraction.

### The Role of Diffraction

- Diffraction spreading angle is proportional to $1/d$
- Small fog droplets cause wide diffraction patterns, leading to color overlap and a white appearance
- Large raindrops lead to narrow diffraction, preserving distinct colors.

### Angular Positions

- Primary rainbows are seen around 40{o} to 42{o} from the anti-solar point
- Fogbows are seen at approximately 140{o} (due to double internal reflection and scattering angles)
- The secondary bow angles are around 138{o} (for fogbows) versus $\sim$50{o} to 54{o} for regular rainbows.

### Color and Supernumerary Bows

- Fogbows appear white because the diffraction causes colors to blur together
- Diffraction also creates concentric supernumerary bows, which are much more visible in fogbows due to the small droplet size.

![Screenshot at 0:04: A pale, white arc observed in a foggy field, visually defining the fogbow phenomenon.](https://ss.rapidrecap.app/screens/OEQeSrXy-YA/00-00-04.png)
![Screenshot at 0:13: A hand-drawn comparison showing a faint, gray arc next to a colored rainbow, illustrating the lack of color in a fogbow.](https://ss.rapidrecap.app/screens/OEQeSrXy-YA/00-00-13.png)
![Screenshot at 0:39: A diagram showing light rays reflecting off a spherical water drop at $\\sim 140{o}$, illustrating the reflection angle relevant to fogbows.](https://ss.rapidrecap.app/screens/OEQeSrXy-YA/00-00-39.png)
![Screenshot at 0:58: A stick figure diagram showing the required geometry for a rainbow: sun, observer, and raindrops creating a 42{o} angle for red light.](https://ss.rapidrecap.app/screens/OEQeSrXy-YA/00-00-58.png)
![Screenshot at 1:31: A hand-drawn representation of wave interference patterns \(bright/dark spots\) created by light passing through two slits, analogous to diffraction.](https://ss.rapidrecap.app/screens/OEQeSrXy-YA/00-01-31.png)
![Screenshot at 1:43: A simulation showing multiple concentric, colored rings instead of a single rainbow band, illustrating the effect of diffraction.](https://ss.rapidrecap.app/screens/OEQeSrXy-YA/00-01-43.png)
![Screenshot at 2:16: A comparison between a vivid primary rainbow and the fainter, more complex pattern of supernumerary bows caused by smaller droplets.](https://ss.rapidrecap.app/screens/OEQeSrXy-YA/00-02-16.png)
![Screenshot at 3:16: A side-by-side plot comparing the simulation results for large vs. small droplets, showing the color bands merge into white for smaller radii \(droplet sizes\).](https://ss.rapidrecap.app/screens/OEQeSrXy-YA/00-03-16.png)