Rahul Gupta
CS99D: The Science of Art

Photo Essay Project
Illustrations of Some of the Optical Effects Described By M.G.J. Minnaert in
Light and Color in the Outdoors

Freak Reflections (2.12) (Florence)

Although these walls of Orsanmichele are hidden from direct sunlight, there are nevertheless
several strongly illuminated patches apparent on the second and third levels of the outer facade.
The unexpected appearance of sunlight is an indication of a "freak reflection", in which sunlight
has been reflected off of the windows inset into some opposing wall and directed towards the
facade of Orsanmichele.

Window Glass vs. Plate Glass (2.18) (Bologna and Vicenza)

The quality of a pane of glass is oftentimes evident through the properties of images reflected in
its surface. In particular, the skewing and warping of an image reflected in regular window glass
indicates the many irregularities present in the pane itself. By contrast, a sheet of plate glass
usually exhibits a much more consistent reflection, as it is a smoother, more uniform pane.

Light Coils (2.21) (Central Park, New York)

The wavelets present in the lower right-hand corner of this photograph are recognizable because
of the fact that they are outlined in coils of light. When the light source is high above the viewer
(as is the sun in this example), and the wavelet is observed at a relatively large angle relative to
the horizontal, light reflecting off of both the bridge and trough of the undulation merges
together in its path towards the eye of the viewer. In such instances, the region between trough
and bridge is reflected towards the viewer, and a light coil may be observed. It is also possible to
recognize the reflections of the dark branches of trees present on the far bank, which appear as
"capricious kinks, knots, and coils" (Minnaert 33).

The Dominance of Vertical Lines in Reflections (Vicenza)

As noted in Light and Colour in the Outdoors, "in the case of an upright line, the columns are
neatly stacked together and magnify each other . . . [while] in the case of a horizontal line, they
lie side by side and broaden the line to a hazy surface" (Minnaert 26). The assertion is visible in
this photograph of the Ponte degli Alpini and the surrounding buildings of Bassano del Grappa.
Note the reflections of the buildings in the river. Of particular interest is the fact that the
reflections of the black rectangular windows merge into vertical lines, while the lighter areas of
wall between windows are lost.

Streetlight Columns in the Arno River (2.20) (Florence)

Once again, we may observe how the reflection of light assumes the form of a vertical column
when projected upon the surface of a body of water. In this example, streetlights placed on the
waterfront are forming columns in the Arno River below. The columns of light are
produced by reflections in eddies formed by the play of wind about the water's surface.
Furthermore, it is also possible that the light is reflecting off of the countless particles of dirt
present in the Arno River, and that the columns of light would be visible even if the wind was
nonexistent. Note that all of the columns lie along a vertical line through the source of light and
the eye of the observer. This is not always the case, and deviations oftentimes occur when factors
such as wind are present.

The Setting Sun Reflected in a Vertical Column Across the Sea (2.23) (Venice)

In these examples, the columns of light are produced by the rays of the setting sun. Minnaert's
analysis tell us that "the ratio of the apparent length to the breath of the light path is . . . sin w",
where w is the angle formed between the plane of the sea and a line drawn from the eye to the
approximate center of the column (Minnaert 29). Minnaert's assertion as to the ratio of length to
breadth is with respect to the reflection seen on one individual wavelet on the ocean surface.
Thus, these reflected pillars of sunlight are the result of the "stacking" of each wavelet's thin
reflected column. These individual columns tend to reinforce each other along the vertical axis,
resulting in a pillar of light that extends towards the horizon. By contrast, the reflective columns
fail to support each other along the horizontal axis, and thus one typically does not obsreve any
appreciable column of light extending in the horizontal direction. The reason that reinforcement
occurs along the vertical axis is that the light reflected by a series of waves along this axis will
all point in the same direction, that is, along a line from the source to the eye of the observer. By
the same logic, the majority of the light reflected by a wave that lies along the horizontal axis
and to one side of the observer's direct line-of-sight will fail to reach the eye of the observer, as
its path of reflection will lie primarily along a line extending through the source of light and the
wavelet itself. The applicability of this logic with respect to individual observations varies greatly, and
factors such as wind may help account for the cone of light visible in the second photograph.

A Reflection of the Setting Sun in the Sea (2.23) (San Giorgio, Venice)

In these photographs, it is possible to sea a dimmed reflection of the reddish, setting sun in the waters
below. Such a reflection is visible because of the reflective properties of the waves. In such conditions
as are present here, only the waves nearest the horizon reflect the sunlight at an angle that is sufficient
for the observer's eye.

The Reflective Properties of Rain (2.27) (Florence)

These pictures, obtained at the end of a day of intermittent rain, illustrate how columns of light
may also be observed on slick roadways. In these examples, the headlights of a passing car and
the surrounding street lamps cast columns of light upon the road. Furthermore, the remnants of
this rainy day also illustrate how a smooth patch of water, untroubled by passing breezes,
oftentimes demonstrates excellent reflective properties. In the second example, the neon
Pizzeria sign hanging from an adjacent storefront is clearly discernible.

The Light and Color of the Sky (11.196) (Pienza)

These photos provide fine examples for observing how the colors of a landscape shift towards
bluish-white as the distance from the viewer increases. This shift occurs when rays of light
scatter upon intersecting small particles of dust present in the air. Minnaert notes that such a
scattering causes the contrast between different parts of a distant scene to be lessened, and the
resulting "background [tends to be] more uniform and also more blue" (Minnaert 263).

The Scattering of Light By Airborne Particles (11.208) (Citta Alta, Bergamo)

This solitary photo demonstrates how particles of dust present in the air allow one to trace out
the path of the sunlight. Here we may observe extremely faint lines extending from the upper-left
to the lower-right corners of the scene.

The Scattering of Light By Clouds (11.209) (Viareggio)

Here the sun's disk as been partially hidden by a mass of clouds. If we look closely, it is
possible to discern at lesast four distinct bands of sunlight emanating outwards through patches in
the clouds. By reflecting off of particles of dust present in the air, these rays reveal the paths they
trace in the skies above the beaches of Viareggio.

Minnaert, M.G.J. Light and Color in the Outdoors. New York: Springer, 1974.

Where applicable, a note of the form (Chapter.Section) has been used to indicate a picture's
relation to the observations described in Minnaert's book.