Photographing Rainbows and the Anti-Solar Point AI-pedia

Photographing a rainbow requires an understanding of meteorology, geometric optics, and camera mechanics. A rainbow is not a physical object located at a fixed position in space; rather, it is an optical phenomenon created by the refraction, internal reflection, and dispersion of light within airborne water droplets. Because a rainbow is an apparent image formed along a specific angular cone relative to the observer, its location changes whenever the observer moves. Every individual observer—and every camera lens—sees a unique rainbow centred entirely around their own visual axis.

The geometric anchor of any rainbow is the anti-solar point. The anti-solar point is the exact point on the celestial sphere directly opposite the Sun relative to the camera lens. Because the primary rainbow forms an arc with an angular radius of approximately 42 degrees centred on this point, the anti-solar point always occupies the exact geometric middle of the full rainbow circle. Consequently, whenever the Sun shines directly onto the back of the camera to illuminate rain in front of it, the shadow of the camera and the photographer is projected straight toward the anti-solar point.

Capturing a rainbow with a camera introduces specific technical challenges. Photographers must manage an optical formation that spans over 80 degrees of the sky, resolve exposure imbalances between bright sky and dark storm clouds, handle the heavy linear polarisation inherent to droplet reflections, and prevent their own projected shadows from marring the composition. Overcoming these constraints requires deliberate lens selection, careful terrain positioning, and an understanding of how light behaves inside spherical droplets.

The Geometry of the Anti-Solar Point

The anti-solar point (sometimes written as the antisolar point) is defined as the point located 180 degrees away from the Sun along the line connecting the Sun and the observer. If a straight line is drawn starting at the centre of the solar disc, passing directly through the entrance pupil of the camera lens, and continuing outward into the landscape, that line terminates at the anti-solar point. In spherical coordinates, if the Sun is at an azimuth of $\theta$ and an altitude of $h$, the anti-solar point lies at an azimuth of $\theta \pm 180^\circ$ and an altitude of $-h$.

This coordinate relationship dictates whether a rainbow can be seen above the astronomical horizon from level ground. When the Sun is at the horizon (a solar altitude of 0 degrees), the anti-solar point lies exactly on the opposite horizon. In this condition, the upper half of the 42-degree primary rainbow arc is visible in the sky, forming a semicircle. As the Sun rises higher in the sky, the anti-solar point sinks correspondingly further below the horizon. As a result, the visible portion of the rainbow arc shrinks.

When the Sun reaches an altitude of 42.3 degrees, the apex of the primary rainbow touches the horizon. If the Sun climbs above 42.3 degrees, the entire primary rainbow drops below the horizon and becomes invisible to an observer standing on flat terrain, because there are no airborne raindrops between the observer's eyes and the ground to complete the optical path. For this reason, primary atmospheric rainbows are primarily morning and late afternoon phenomena in temperate and tropical latitudes.

The secondary rainbow, which has an angular radius of approximately 51 degrees, remains visible until the Sun reaches an altitude of approximately 53 degrees. Between solar altitudes of 42.3 degrees and 53 degrees, it is possible to observe an "orphaned" secondary rainbow where the outer arc appears in the sky without the brighter primary arc beneath it.

Solar Altitude	Anti-Solar Point Altitude	Primary Arc Apex Height	Secondary Arc Apex Height	Visible Arc Shape (Level Ground)
0° (Sunrise/Sunset)	0° (On horizon)	42° above horizon	51° above horizon	Full semicircle (180° arc)
10°	-10° (Below horizon)	32° above horizon	41° above horizon	Large arc (approx. 150°)
20°	-20° (Below horizon)	22° above horizon	31° above horizon	Moderate arc (approx. 120°)
30°	-30° (Below horizon)	12° above horizon	21° above horizon	Low arc (approx. 90°)
42.3°	-42.3° (Below horizon)	0° (On horizon)	8.7° above horizon	Only secondary bow visible
> 53.5°	< -53.5° (Below horizon)	Below horizon	Below horizon	No rainbow visible on flat land

Optical Structure of the Rainbow

The visual properties of a rainbow are governed by Descartes' laws of refraction and reflection within roughly spherical water droplets. Light entering a droplet slows down and refracts (bends) at the air-water boundary. The light then travels across the droplet, undergoes partial internal reflection at the rear interior surface, and refracts again as it exits back into the air toward the viewer.

The Primary Arc

The primary rainbow is formed by rays of light that experience one internal reflection inside the water droplet. Dispersion occurs because different wavelengths of light refract at slightly different angles: liquid water has a higher refractive index for short violet wavelengths ($n \approx 1.344$) than for long red wavelengths ($n \approx 1.331$). As a result, red light emerges at a maximum deflection angle of 42.3 degrees from the anti-solar point, while violet light emerges at an angle of 40.5 degrees.

This differential deflection causes the primary arc to appear with red on the outside and violet on the inside. Because 42 degrees represents a caustic limit—a mathematical concentration of exiting light rays—the sky directly inside the primary arc is notably brighter than the sky outside it. Droplets inside the 42-degree cone continue to scatter unseparated white light toward the camera, producing a bright, luminous white glow within the inner disc of the bow.

The Secondary Arc and Alexander's Dark Band

The secondary rainbow is produced when incoming light undergoes two internal reflections inside each water droplet before exiting. Because energy is lost at each internal reflection, the secondary bow is dimmer than the primary bow, retaining roughly 43 percent of the primary arc's surface brightness. The second internal reflection reverses the order of the colours, placing red on the inner edge (at roughly 50.5 degrees) and violet on the outer edge (at roughly 53.5 degrees).

Between the primary and secondary arcs lies an area of the sky known as Alexander's dark band, named after the Greek philosopher Alexander of Aphrodisias, who first described it in 200 AD. In this region, no single-reflection rays can exit above 42.3 degrees, and no double-reflection rays can exit below 50.5 degrees. Because geometric optics prevents direct droplet reflection into this annular gap, the sky between the two bows appears distinctly darker than either the exterior sky or the interior of the primary bow.

Supernumerary Arcs

On the inner fringe of the primary rainbow, faint, narrow bands of pastel green, pink, or purple are sometimes visible. These are supernumerary arcs. They cannot be explained by classical ray optics and require wave optics (the wave theory of light) to understand. Supernumerary arcs are interference fringes caused by light waves that travel along slightly different paths through identically sized droplets and recombine either in phase (constructive interference) or out of phase (destructive interference). Photographing clear supernumeraries requires rain showers with uniform droplet sizes, typically between 0.5 and 1.0 millimetres in diameter.

The Shadow Paradox in Composition

Because the anti-solar point is located directly opposite the Sun, it marks the exact direction where any object standing between the Sun and the landscape casts its shadow. If a photographer sets up a tripod to photograph a low rainbow, the shadow of the camera, tripod legs, and the photographer's head will be projected directly toward the geometric centre of the rainbow circle.

This geometric reality creates a common compositional problem: in wide-angle landscape photography, the photographer's own shadow frequently intrudes into the lower portion of the frame. The visibility and sharpness of this shadow depend on the distance between the camera and the ground, the angle of the terrain, and the nature of the umbra and penumbra.

Umbra and Penumbra Dynamics

The Sun is not a single point of light; it has an angular diameter of approximately 32 arcminutes (about 0.53 degrees). Because of this non-zero width, shadows cast by sunlight consist of two parts:

• Umbra: The central, darkest zone of the shadow where the solar disc is completely blocked. The umbral cone tapers down over distance. The length of an object's umbral cone is equal to its physical diameter divided by $2 \times \tan(0.265^\circ)$, which is roughly 108 times the diameter of the object. For a camera body and lens with an effective width of 12 centimetres, the umbra extends approximately 13 metres. Beyond 13 metres, the lens has no true umbra.
• Penumbra: The outer region of the shadow where the Sun is only partially obscured. The penumbra widens with distance, causing the edges of the shadow to become softer and lower in contrast as the distance from the camera to the ground increases.

If the anti-solar point falls on foreground ground located 2 to 5 metres from the lens, the shadow of the camera and photographer will be sharp, high-contrast, and clearly identifiable in the image. If the anti-solar point falls onto a distant valley floor 500 metres away, the camera's umbra has completely dissipated, and the penumbra is so faint and dispersed that it is invisible to the camera sensor.

Techniques for Eliminating or Concealing the Shadow

Photographers employ several practical strategies to remove, hide, or avoid casting a shadow when capturing the anti-solar region of a rainbow.

1. Elevation and Foreground Geometry

The most straightforward method to hide the shadow is to eliminate the physical surface upon which it can be projected:

• Photographing over drops: Standing on the edge of a cliff, ridge, balcony, or steep slope allows the line of sight to pass into open air. If there is no ground in the immediate foreground, the shadow is cast into the distant air or onto ground far below, where optical dispersion makes it invisible.
• Water foregrounds: If the foreground consists of deep, dark, or moving water, the shadow is not clearly projected. Light penetrates into clear or moving water rather than scattering sharply off a planar surface, eliminating the distinct silhouette of the photographer.

2. Physical Elevation and Decoupled Triggering

When working on flat, open terrain, the photographer can physically separate their body from the camera's optical axis:

• High tripod mounting: Raising the camera on a centre column or tall tripod (2 to 3 metres high) pushes the shadow of the camera further away along the anti-solar vector, while the photographer steps several metres laterally to the side. The camera is then triggered using a wireless remote, a smartphone app, or an intervalometer. The photographer's personal shadow is moved completely outside the field of view, leaving only the minimal, thin silhouette of the tripod legs and camera body.
• Crouching or sitting: If shooting hand-held or from a standard tripod height, crouching directly behind the camera minimizes the vertical cross-section of the photographer. Dropping the camera close to the ground reduces the distance the shadow travels, projecting it into the immediate foreground weeds or gravel directly beneath the front lens element, where it falls outside the lower boundary of the frame.

3. Environmental Masking

Photographers can use pre-existing shadows in the landscape to swallow the camera's shadow:

• Terrain and vegetation shadows: By positioning the tripod inside the shadow cast by a large boulder, a tree line, a vehicle, or a building, the camera itself is in shadow. If direct sunlight does not strike the camera or photographer, they cannot cast a secondary shadow into the frame. As long as the rain shaft remains illuminated by direct sunlight in front of the camera, the rainbow will remain fully formed.
• Topographical hollows: Placing the camera in a slight dip or depression allows the surrounding terrain to catch the shadow before it reaches the area covered by the wide-angle frame.

4. Lens Shift and Optical Decentering

Perspective-control lenses (tilt-shift lenses) provide an optical method for evading the anti-solar shadow:

• A tilt-shift lens allows the optical elements to slide parallel to the image sensor plane. By keeping the camera body level and shifting the lens upward, the photographer moves the field of view upward into the sky without tilting the camera back.
• This shifting motion places the geometric centre of the sensor below the optical axis of the lens. The anti-solar point (which aligns with the optical axis) can be repositioned at or below the bottom border of the physical photograph, cutting the photographer's shadow out of the frame while preserving the full upper arch of the rainbow.

5. Digital Post-Processing Removal

When physical avoidance is impossible, digital correction during post-processing is a standard alternative. Photographers can capture two frames: one primary exposure, and a second exposure where they step slightly to the side or alter the tripod's position. Using clone stamping, content-aware fill, or manual layer masking in photo editing software, the undisturbed ground from the alternate shot can be blended over the shadow.

Lens Selection and Field of View

Capturing a rainbow requires careful consideration of focal length because of the vast angular size of the phenomenon. A primary rainbow has an angular diameter of approximately 84 degrees ($2 \times 42^\circ$), while a full double rainbow extends across roughly 106 degrees ($2 \times 53^\circ$).

Focal Length (Full-Frame Equivalent)	Horizontal Field of View	Vertical Field of View	Diagonal Field of View	Rainbow Framing Capabilities
11 mm (Rectilinear)	117°	95°	126°	Captures full double rainbow with foreground in horizontal orientation
14 mm (Rectilinear)	104°	81°	114°	Captures full primary bow easily; cuts edges of secondary bow horizontally
16 mm (Rectilinear)	97°	74°	107°	Captures full primary bow with careful composition; cuts secondary bow
20 mm (Rectilinear)	84°	62°	94°	Barely fits the 84° primary bow edge-to-edge diagonally; truncates horizontally
24 mm (Rectilinear)	74°	53°	84°	Cannot capture entire primary arc in one shot; ideal for details or segments
15 mm (Fisheye)	180° (Diagonal)	Variable	180°	Captures complete double rainbow and environment with barrel distortion

Rectilinear Versus Fisheye Lenses

Rectilinear lenses are optical designs that preserve straight lines, preventing them from curving in the final photograph. However, when ultra-wide rectilinear lenses (such as 12mm to 14mm on full-frame sensors) are used, they suffer from optical stretching toward the edges and corners of the frame, known as geometric distortion or wide-angle keystoning. This stretching causes the circular arc of a rainbow to appear deformed, flattening it into an ellipse near the edges of the frame.

Fisheye lenses map angles directly to radial distances on the sensor, rather than projecting onto a flat plane. A fisheye lens preserves the true angular width and uniform curvature of the rainbow circle across the entire frame. However, this causes straight lines in the landscape (such as the horizon or architectural features) to curve dramatically unless they pass directly through the centre of the frame. For scientific or full-sky meteorological documentation, fisheye lenses are preferred; for traditional landscape aesthetics, rectilinear lenses are more common.

Panoramic Stitching

When an ultra-wide lens is unavailable, or when higher image resolution is required, photographers construct rainbow panoramas by stitching multiple overlapping exposures taken with a standard lens (such as a 35mm or 50mm prime). However, rainbow stitching introduces three significant optical challenges:

• Parallax error: The camera must be rotated around the lens's entrance pupil (often incorrectly called the nodal point). If the camera rotates around the tripod mount, nearby foreground elements will shift relative to the distant background, causing stitching seams to misalign.
• Droplet and cloud motion: Because rain shafts and clouds drift rapidly in the wind, long delays between individual frames can cause the rainbow's brightness or colour to shift, creating visible bands or discontinuities where adjacent panels join.
• Projection mapping: Panoramic stitching software typically projects photographs onto a cylindrical or equirectangular coordinate system. Selecting a planar (rectilinear) projection for an 84-degree panorama results in severe stretching at the boundaries. Choosing a cylindrical or spherical projection keeps the rainbow's arc visually natural and uniform.

Polarisation and Filter Dynamics

The interaction between rainbow light and optical filters—particularly circular polarising filters (CPLs)—is one of the most critical considerations in rainbow photography. Rainbow light is not unpolarised natural light; it is highly linearly polarised.

The Brewster Angle Mechanism

When sunlight strikes the back inside surface of a spherical water droplet, the angle of incidence is roughly 40 degrees. The Brewster angle (the angle of incidence at which light with a particular polarisation is perfectly transmitted rather than reflected) for an internal water-air interface is approximately 37 degrees. Because the angle of incidence inside the droplet is exceptionally close to Brewster's angle, light polarized parallel to the plane of incidence is largely refracted out through the back of the drop and lost.

Consequently, the light that successfully reflects internally and emerges toward the observer is up to 94 percent linearly polarised perpendicular to the plane of incidence. In geometric terms, this means the electric field vector of rainbow light is oriented tangentially along the curvature of the arc at every point:

• At the top of the rainbow arc, the light is polarised horizontally.
• At the vertical sides (the bases) of the rainbow arc, the light is polarised vertically.
• At any intermediate 45-degree section, the polarisation axis tilts at 45 degrees.

Effects of Polarising Filters

Because the polarization axis changes direction along the circumference of the bow, a linear or circular polarising filter cannot uniformly enhance an entire rainbow. Rotating a polariser produces distinct, contradictory results:

• Cancelling the arc: If the polariser is rotated to block horizontally polarised light, the top of the rainbow will completely vanish from the photograph, while the vertical sides of the bow will remain visible and gain contrast against the background sky.
• Cancelling the sides: If the polariser is rotated 90 degrees to block vertically polarised light, the vertical sides of the rainbow will disappear entirely, while the top of the arch will brighten and intensify.
• Contrast enhancement: Unpolarised background light scattered by clouds or air molecules can be attenuated by a polariser, which often makes a selected section of the rainbow stand out vividly. However, an ultra-wide angle shot of an entire rainbow through a polarising filter will inevitably show uneven intensity: some parts of the arc will be suppressed, while other parts are saturated.

For this reason, landscape photographers generally avoid using polarising filters when attempting to capture a complete, balanced rainbow arc in a single wide-angle exposure, or they use the polariser conservatively at an intermediate rotation angle.

Neutral Density Filters

Graduated Neutral Density (GND) filters are widely used to manage high dynamic range. During a rainbow event, the sky behind the rainbow is often dark and stormy, while the ground or clouds illuminated by direct sunlight can be exceptionally bright. A soft-edge graduated neutral density filter can be positioned over the upper or lower half of the frame to balance exposure without disrupting the rainbow's natural colour saturation.

Exposure and Colour Capture

Rainbows are transparent, luminous phenomena; they do not have a fixed physical brightness of their own, but rather add their light to the background sky. Successfully capturing their colour requires precise exposure control and colorimetric processing.

Metering and Dynamic Range

Modern digital cameras equipped with evaluative or matrix metering systems can be misled by the high contrast of a rainbow scene. If the camera meters for the dark storm clouds in the background, it will overexpose the image. Overexposure causes the delicate, highly saturated colours of the rainbow to clip (saturate the red, green, or blue colour channels), turning the rainbow into a washed-out white band.

To avoid clipping:

• Photographers rely on the camera's raw histogram, specifically checking the individual RGB channels rather than a single luminance histogram.
• Exposure is set using the "Expose to the Right" (ETTR) method, keeping the brightest highlights just below the clipping threshold, ensuring maximum signal-to-noise ratio in the shadow areas.
• Spot metering can be performed directly on the brightest portion of the primary arc to assess its luminance relative to the foreground.

Raw File Processing

All rainbow photography intended for high-fidelity reproduction should be recorded in an uncompressed 14-bit or 16-bit raw file format. In raw conversion software:

• White balance: Rainbow colours are anchored relative to daylight. A daylight white balance preset (5500K to 6500K) preserves natural chromaticity. Setting the white balance to "Auto" can cause the camera to shift colour temperature frame-to-frame as storm clouds drift, altering the perceived hue of the rainbow.
• Dehaze and Clarity: Algorithms that adjust local contrast (such as "Dehaze" or "Clarity") operate by detecting subtle differences in atmospheric attenuation. Applying moderate amounts of dehazing can significantly enhance the visibility of faint secondary and supernumerary arcs against cloudy skies, though excessive adjustments produce unnatural dark halos around the edges of the arc.
• Vibrance versus Saturation: Vibrance adjustments apply non-linear saturation increases that protect already saturated colours while boosting muted mid-tones. This helps bring out faint greens and violets in the primary arc without oversaturating the red channel.

Specialised Variations and Related Optical Phenomena

Understanding the anti-solar point allows photographers to identify and photograph other related optical phenomena that occur under specific atmospheric or meteorological conditions.

Red Rainbows (Sunset and Sunrise Rainbows)

When a rainbow occurs while the Sun is directly on the horizon, sunlight must pass through a long, dense column of the Earth's atmosphere. Rayleigh scattering scatters away the shorter wavelengths of light (blue, violet, and green). As a result, only long red and deep orange wavelengths reach the water droplets. The resulting rainbow is monochromatic or dichromatic, appearing as an intense red or crimson arc with no blue or violet bands.

Full-Circle Rainbows

From level ground, the Earth blocks the lower half of the 42-degree cone of light. However, if an observer is elevated high above the ground—such as inside an aircraft, atop a skyscraper, or standing on a narrow mountain peak—and airborne water droplets exist both above and below the horizon line, the full 360-degree circle of the rainbow can be seen. The anti-solar point sits dead centre inside the circle. In aircraft photography, the shadow of the aeroplane itself is visible at the exact centre of the full-circle rainbow if the cloud or mist layer is close enough.

Fog Bows

A fog bow (sometimes called a white rainbow) is formed by much smaller water droplets—typically fog or cloud droplets with diameters smaller than 0.05 millimetres (50 micrometres). When droplets are this small, diffraction dominates over classical refraction and geometric reflection. Diffraction broadens the scattered rays and causes different colours to overlap and wash out, producing a broad, ghostly white arc with a faint reddish outer border and a bluish inner edge. Fog bows also have a radius of roughly 42 degrees centred on the anti-solar point.

Glories

A glory is an optical phenomenon that is frequently confused with a miniature full-circle rainbow. A glory consists of one or more concentric, brightly coloured rings centred directly on the anti-solar point. Unlike a rainbow, which has a 42-degree radius, a glory is much smaller, with an angular radius typically ranging from 1 to 5 degrees. Glories are produced exclusively by wave interference and diffraction from droplets between 10 and 30 micrometres in diameter. They are commonly photographed from aircraft, or from high mountain ridges when the photographer's shadow is cast onto a lower cloud deck (a phenomenon known as the Brocken Spectre).

Dew Bows

Dew bows form when droplets of water resting on horizontal surfaces—such as dewy grass, spiderwebs, or wet sand—scatter sunlight back toward the camera. Because the droplets lie on a horizontal plane rather than being distributed throughout a three-dimensional volume of air, the intersection of the 42-degree cone with the flat ground produces a conic section: a hyperbola, parabola, or ellipse depending on solar elevation. The axis of the dew bow remains mathematically locked to the anti-solar point, but its shape on the ground is distorted by the surface geometry.

Historical and Scientific Observations

The anti-solar geometry of the rainbow has been investigated mathematically for centuries:

• Theodoric of Freiberg (c. 1250–c. 1310): In his treatise De iride et radialibus impressionibus (c. 1304–1311), Theodoric correctly deduced that the primary rainbow is formed by individual droplets undergoing two refractions and one internal reflection, identifying the role of the observer's eye as the apex of the visual cone. Persian polymath Kamal al-Din al-Farisi reached the same conclusion independently around the same period.
• René Descartes (1596–1650): In his 1637 work Discourse on the Method (specifically the appendix Les Météores), Descartes applied Snell's law of refraction to trace thousands of individual light rays through a spherical water droplet. He mathematically derived the 42-degree primary angle and 51-degree secondary angle, establishing the theoretical foundation of rainbow geometry and proving why the centre of the arc must lie directly opposite the Sun.
• Isaac Newton (1642–1727): In his 1704 work Opticks, Newton demonstrated that white light is a mixture of spectral colours and explained that the rainbow's chromatic bands are caused by the differing refractive indices of each colour in water.
• George Biddell Airy (1801–1892): Airy developed the mathematical equations describing the diffraction of light in rainbows, accurately predicting the formation and spacing of supernumerary arcs based on droplet size.

Long-Duration Observations

Atmospheric stability, continuous precipitation, and persistent sunlight are required for a rainbow to endure over long periods. The official Guinness World Record for the longest-lasting rainbow observation occurred on 27 November 2017 in the Yangmingshan mountain range in Taipei, Taiwan. Observers at the Chinese Culture University documented a rainbow that persisted continuously for 8 hours and 58 minutes, from 06:57 to 15:55. This prolonged duration was made possible by a seasonal winter monsoon that trapped steady moisture and cloud cover over the mountain basin while clear sunlight streamed past the terrain from the south.

Summary of Practical Photographic Guidelines

1. Locate the anti-solar point: Stand with your back squarely to the Sun; your head's shadow points directly toward the geometric centre of the rainbow.
2. Assess solar elevation: If the Sun is higher than 42 degrees in the sky, do not look for a primary rainbow in the sky from flat ground; it is below the horizon. Wait for late afternoon or early morning.
3. Select focal lengths: Use a 14mm to 16mm ultra-wide lens (full-frame equivalent) to capture the full primary arc; use an 11mm or fisheye lens to fit a double rainbow into a single shot.
4. Control the shadow:
   • Crouch low or position the tripod close to foreground elements to push the shadow out of frame.
   • Elevate the camera on a tall tripod, trigger it remotely, and step aside.
   • Position the setup in the shade of a tree, building, or vehicle so no personal shadow is cast.
   • Use a tilt-shift lens to raise the framing optically without tilting the camera axis.
5. Use polarisers carefully: Be aware that a circular polarising filter will darken or completely erase portions of the rainbow arc depending on its rotational angle due to the tangential linear polarisation of droplet reflections.
6. Expose for the highlights: Monitor individual RGB histograms to prevent clipping the red channel in the bright primary arc.

See also

• Alexander's dark band
• Atmospheric optics
• Brewster's angle
• Brocken spectre
• Circular polarising filter
• Dispersion (optics)
• Fog bow
• Glory (optical phenomenon)
• Moonbow
• Rayleigh scattering
• Supernumerary rainbow