Since I used a long focal length lens (300 mm) to isolate the end of this rainbow the angular width of the rainbow is a significant fraction of the angular field of view. If instead, I had used a wide angle lens (e.g., 16 mm focal length) the end of the rainbow would have been tiny in the composition.
Rainbows are best described in terms of angles. The arc of the primary rainbow has an angular radius of 42-degrees or a diameter of 84-degrees. The secondary rainbow has an angular radius of 51-degrees ( a 102-degree diameter).
A rainbow is not located at a place; instead, it is seen along a well-defined angle from your location. The thickness, or width, of the colors we see in a rainbow, are also defined by an angular measurement.
The width of the colored band of the primary rainbow is about 2-degrees. The angular field of view of the 300 mm lens I used to take this photograph is 6.8 x 4.5 degrees. Since the format of this photograph is portrait mode, the rainbow’s 2-degree width looks very big in the relatively narrow 4.5-degree angular field of view of the 300 mm lens.
Why is this Rainbow so Bright and Where is the Blue?
The rainbow in this photo is very bright due to a few factors.
- Larger raindrops produce brighter, more saturated colors.
- Large raindrops close to the ground become flattened as they fall, this results in the rainbow having a bright base.
- The light from the rainbow is highly polarized, and a polarizing filter was used.
Raindrop Size
Firstly, rainbows are brighter near their base due to larger raindrops mixed in with smaller raindrops closer to the ground. Larger raindrops, 1 mm or more in diameter, produce brighter colors in a rainbow. Larger raindrops also produce brighter reds, greens, and violets than blues. Smaller raindrops weaken the reddish colors. In this photograph, the bright reds and little blues are a good indicator of very large raindrops.
When the droplets become smaller, like in a mist, all colors except violet can disappear. Very fine mists (fog) with water droplets less than 0.05 mm in diameter, produce rainbows where all the colors overlap, resulting in a white rainbow, known as a “fogbow”.
Raindrop Shape
As raindrops fall they enlarge. When the raindrop gets to on order of a. few millimeters or more they tend to break up due to collisions with other raindrops and frictional forces as they fall through the air. Before the larger raindrops break up they become distorted into flattened spheres. These distorted raindrops refract and reflect more light to the sides and base of the rainbow then they contribute to the top of the bow. The fainter rainbow near the top results from smaller spherical drops.
The Polarization of the Light From a Rainbow
Light is an electromagnetic wave with oscillating electric and magnetic fields. These fields oscillate perpendicular to each other and to the direction the light travels. Waves like this are referred to as “transverse waves”. The orientation of the electric field oscillations in the plane perpendicular to the direction light travels is known as the polarization of the light.
Most sources of light generate a random mixture of waves with different frequencies, phases, and polarizations. This light is referred to as unpolarized light. Unpolarized light can become polarized as it passes through a special filter that only passes electric field oscillations along a particular angle (a picket fence analogy for the filter helps).
Light also becomes partially polarized upon reflection from a surface and refraction through an interface. When rays from the sun reflect from the back surface of a raindrop they become polarized. The amount of polarization depends upon the angle of reflection. For a special angle of reflection, known as the Brewster Angle, the reflected is totally polarized along one direction, parallel to the surface. The angle of reflection from the back surface of a raindrop is close to the Brewster Angle, resulting in highly polarized light forming the rainbow.
If we look at a rainbow through polarizing sunglasses or use a polarizing filter on a lens, we can rotate the polarizer so only the polarized rainbow passes (making the rainbow very bright), or rotate it so the rainbow disappears. The white light inside the arc of the rainbow is also highly polarized since it too reflects from the backside of the raindrop.
The blue sky far from the rainbow is also polarized due to scattering from air molecules; this is especially true perpendicular to the sunlight. By adjusting the angle of a polarizing filter you can brighten the light from the rainbow while also darkening the sky around it, thereby improving the contrast of the rainbow.
