In childhood one would have enjoyed making butterfly, bird, dog etc. using hand-shadow. Some movies with horror/thriller/suspense genre use “shadow” as a creepy concept in from of “Shadow Person”. Due to this “shadow person” I myself faced difficulty in sleeping alone at night. But today, as a matured person, I will discuss the scientific aspects of what we call “shadow”.
As you may already know from your high-school science course that “shadow” is produced on a screen behind the object when light from a source is blocked (either completely or only partially) by the object. Note that, it is appropriate to construct the shadow using simple straight-line rays only if the optical waves (light has two characters: wave and particle!) can be treated as simple straight-line rays (called geometrical optics). If you look at your own shadow on the ground; the shadow of your feet is sharp, the shadow of your head is not. Similarly, the shadow of the bottom part of a tree-trunk or post is sharp, whilst the shadow of the higher parts becomes more and more hazy towards the top. These peculiarities are likewise a consequence of the sun’s not being a mere point. Moreover, the shadow of a butterfly, of a bird (ever noticed?) looks like a round spot. For some interesting “shadow on snow” photos see .
A clear unambiguous shadow (which I call “perfect shadow”) requires a source of light that either is very small compared to the dimensions of the object or else is very far away (called “point source”). In real life, we generally encounter perfect shadows during day time, because Sun (our star!) being very far away from us, acts “like” a point source.
False (perfect) shadows (most of times along with the lengthening shadows) are used to make a flat image appear “3-dimensional”. This works because our eyes are accustomed to the idea that a shadow is produced when an object is in front of a screen . Also, as an object moves away from source of light, the shadow lengthens faster and faster. This follows from simple geometrical properties of rays (can be explained using “elementary-trigonometry”).
But at night, we seldom get perfect shadows. This is because the general source of light at night is street-light (no celestial body at night is bright enough to cast shadow on earth, see ). Now street-light (generally sodium-lamp in India and LED-lamp in developed countries) may be too near/large to be regarded as a “point source”, we call such sources of light “extended sources”. For extended sources, the shadow is constructed using the “principle of superposition”, where the extended source is modeled as a large number of point sources, and the shadow produced by each of these point sources is constructed independently, then the light striking a screen behind the object is the sum of the contributions from all of the light sources taken individually. Also, the shadow produced by two or more point sources can be understood by the principle of superposition in the same way. This superposition leads to two regions of shadow,
- umbra: the portion of the shadow which is totally dark because light from all sources is absent;
- penumbra: the portion of the shadow which is illuminated by some of the sources and is therefore not completely dark.
This ambiguity in shadow boundaries caused due to superposition, leads to what we perceive as creepy effects of shadow at night. But, this ambiguity in boundaries of shadow lead to some very interesting physical effects. Let us analyse some of these effects:
Double Shadow: When the trees have lost their leaves, we may see the shadows of two parallel branches superposed upon each other. A branch quite near to us gives a sharp and dark shadow, one more distant gives a broader and more greyish shadow. If they accidentally fall one upon the other, we see a bright line in the middle of the sharpest shadow, so that this looks double. This phenomenon is called “double shadow”  and will apparently be visible whenever both branches subtend an angle smaller than the sun’s disc.
: A solar eclipse can occur when the Moon passes between Earth and Sun. Thus, a solar eclipse can occur only at New Moon (day). The type of solar eclipse (Partial, Hybrid, Annular & Total) depends upon the region of Moon’s shadow through which a region of Earth passes. The partial solar eclipses are dangerous to look at because the un-eclipsed part of sun is still very bright. The Sun’s distance from Earth is about 400 times the Moon’s distance, and the Sun’s diameter is about 400 times the Moon’s diameter. Because these ratios are approximately the same, the Sun and the Moon as seen from Earth appear to be approximately the same size: about 0.5 degree of arc in angular measure. To see a total solar eclipse, you have to be in just the right spot on the earth, the point where umbra of Moon’s shadow hits Earth. For amazing photos see . In partial solar eclipse the Moon moves in front of the solar disk until only a thin crescent is left. Apart from the awestruck moment of darkness in daytime, the shape of shadows formed by crescent-sun’s light corresponds to the crescent shape. For instance, the shadows of our fingers take on an extraordinary claw-like shape. Similarly, each small dark object throws a crescent-like shadow; the shadow of a small rod consists of a number of such crescents, while
a curvature appears at the ends.
: A lunar eclipse occurs only when the sun, Earth and moon are aligned exactly, or very closely so, in a straight line with the Earth in the middle. Hence, a lunar eclipse can occur only the night of a full moon. The type of lunar eclipse (Penumbral, Partial & Total) depends upon the region of Earth’s shadow through which the Moon passes. For a total lunar eclipse to occur, the direct sunlight should be completely blocked by the earth’s shadow, so the Moon must pass directly behind the Earth into its umbra (shadow). The only light seen on moon’s surface on total lunar eclipse is some light from the Sun refracted through the earth’s atmosphere. This light looks red due to Rayleigh scattering of the more blue light (for the same reason that the sunset looks red). Unlike a solar eclipse, which can be viewed only from a certain relatively small area of the world, a lunar eclipse may be viewed from anywhere on the night side of the Earth. A lunar eclipse lasts for a few hours, whereas a total solar eclipse lasts for only a few minutes at any given place, due to the smaller size of the Moon’s shadow. Also unlike solar eclipses, lunar eclipses are safe to view without any eye protection or special precautions, as they are dimmer than the full moon. For amazing photos see 
Why don’t we have each kind of eclipse once every month (during Full Moon and New moon)? Since the Moon’s orbit around Earth is tipped by about 5 degrees to Earth’s orbit around the Sun, the Moon spends most of the time either above or below the plane of Earth’s orbit.
Earth’s shadow and Belt of Venus at sunrise, seen over a horizon where the sea meets the sky, looking west from Twin Peaks, San Francisco. Note: the lowest blue-grey area is not the sky but the surface of the Pacific Ocean (credit: Brocken Inaglory [CC BY-SA 3.0 or GFDL], via Wikimedia Commons)
: The earth shadow (also sometimes known as the dark segment) is visible from the surface of the Earth, as a low, flat, dark band which stretches for nearly 180° and is bounded below by the horizon and above by the pinkish anti-twilight arch (called “Belt of Venus” ,though it has nothing to do with Venus!). It is the shadow that the Earth itself casts on its atmosphere. It is visible twice a day: in the eastern sky as the sun sets and in the western sky as the sun rises.
Cloud Shadow (credit: NASA Earth Observatory image created by Jesse Allen and Robert Simmon, using Advanced Land Imager data from the NASA EO-1 team, http://goo.gl/AglCqx)
Cloud Shadow: Cloud shadows, in effect the inverse of “Sun rays”, . Sun rays (also called “crepuscular rays”) are rays of sunlight which appear to diverge from the point in the sky where sun is located, because of perspective effect (just like the appearance of parallel railway lines converging at a point). These rays, which stream through gaps in clouds, are columns of sunlit air separated by darker cloud-shadowed regions.
Mountain Shadow: Mountain shadows look triangular regardless of the mountain’s shape when seen from its summit. This is a perspective effect just like “Sun rays”. The finite size of the sun also causes the umbra region of the shadow to converge and eventually taper away and this tapering sets limits to the length of umbra region of the shadows. The limit of the length of umbra region of a shadow for the Earth is over a million miles and for a high mountain it can be two to three hundred miles. Thus, triangular shadows are not seen from objects much smaller than mountains because their shadows are not long enough.
 Marcel Minnaert. De natuurkunde van ‘t vrije veld. L Licht en k1eur in het landschap , B. V. W.J. Thieme & Cie, Zutphen (1937)
I referred to English translation of original German work. Two different English translations are available:
[1(i)] First German edition (1937) translated by “H. M. Kremer-Priest” and revised by “K. E. Brian Jay” under title “Light and Colour In the Open Air” originally published by G. Bell & Sons, Ltd. and republished by Dover Publications Inc. (1954)
[1(ii)] Fifth German edition (1974) translated and revised (added colour photos/ poems to chapters) by “Len Seymour” under title “Light and Color in the Outdoors” and published by Springer-Verlag New York. Inc. (1993)
 Judah Levine. Light and Color (Shadows and geometrical optics), http://www.colorado.edu/physics/phys1230/phys1230_fa01/topic8.html (12 September, 2001)
 James Foster. Objects that case shadow on earth, Science Question of the Week, Goddard Space Flight Center, http://web.archive.org/web/20070627044109/ http://www.gsfc.nasa.gov/scienceques2005/20060406.htm (7 April, 2006)
 Fred Espenak. Lunar Eclipses for Beginners, http://www.mreclipse.com/Special/LEprimer.html (2009)
 Fred Espenak. Solar Eclipses for Beginners, http://www.mreclipse.com/Special/SEprimer.html (2009)
 Ron Hipschman. Why Eclipses Happen, http://www.exploratorium.edu/eclipse/why.html
 Dept. Physics & Astronomy University of Tennessee. Solar Eclipses, Astronomy 161 (The Solar System), http://csep10.phys.utk.edu/astr161/lect/-time/eclipses.html
 Taryn Biggs, Susan McPhail, Kurt Nassau, Hemant Patankar, Margaret Stenerson, Firman Maulana, Michael Douma & Sally E. Smith (Causes of Color). What causes layers in the sunrise and sunset?, http://www.webexhibits.org/causesofcolor/14E.html
 Les Cowley. Cloud Shadows, http://www.atoptics.co.uk/atoptics/clshad.htm
 Les Cowley. Mountain Shadow , http://www.atoptics.co.uk/atoptics/mtshad.htm
 Jeff Filipiak. Watching the snow: images of beauty I find in shadow patterns, http://milwaukeesnow.com/2014/02/13/watching-the-snow-images-of-beauty-i-find-in-patterns/