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How to see shadows in 3D
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2014 Phys. Educ. 49 314
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How to see shadows in 3D
Gea O F Parikesit
Faculty of Engineering, Department of Engineering Physics, Gadjah Mada University,
Jalan Grafika 2, Yogyakarta 55281, Indonesia
E-mail: [email protected]
Abstract
Shadows can be found easily everywhere around us, so that we rarely find it
interesting to reflect on how they work. In order to raise curiosity among
students on the optics of shadows, we can display the shadows in 3D,
particularly using a stereoscopic set-up. In this paper we describe the optics of
stereoscopic shadows using simple schematic drawings. We also describe how
to build a very simple demonstration set-up for casting and displaying
stereoscopic shadows. Moreover, we also describe a list of student activities
that can be used to further raise their curiosity.
Introduction
Shadows can be found easily everywhere around
us [1], so that we rarely reflect on the physics
behind the phenomenon. In order to raise curiosity
about the optics of shadows, we can display the
shadows in three dimensions using a stereoscopic
set-up. In this set-up, each of our two eyes gets
a different view of the same shadow and our
brain merges the two views to create a threedimensional image. Stereoscopic shadows can be
realized experimentally using two pairs of colour
filters, with one pair positioned in front of the light
sources and another pair placed in viewing glasses.
In ‘The optics of stereoscopic shadows’, we
will first describe the optics of stereoscopic shadows using simple schematic drawings. Then, we
will describe how to build a very simple set-up
of stereoscopic shadows. Moreover, we will also
describe a list of student activities that can be used
to further raise their curiosity.
The optics of stereoscopic shadows
The history of people playing with shadows dates
back to at least the second century BCE [2]. In
order to play with shadows, we only need three
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PHYSICS EDUCATION
49 (3)
components: a light source, an object and a screen.
The object can be made from various materials
around us, even including our own hands. The
UNESCO-listed Indonesian art of Wayang Kulit
usually uses a set-up that consists of a light source
using a halogen lamp or a coconut-oil lamp, an
object crafted from buffalo skin and a screen that
is made from a white cotton sheet [3].
Stereoscopic displays have become increasingly popular, both in consumer electronic markets
and in technological applications [4]. A shadow
can also be displayed stereoscopically, as has been
performed by the artist and TED fellow Christine Marie, by using coloured shadows [5]. The
phenomenon of coloured shadows was first documented by Goethe in 1810 [6], where he described
how multiple shadows with various colours can be
cast by using several coloured light sources simultaneously, such that different areas on the screen
display shadows with different colours depending
on how the object blocks light from the coloured
light sources.
Figure 1(a) shows how a pair of coloured
shadows can be cast on a screen. In this example,
two light sources, L1 and L2 , are equipped with red
and cyan filters, respectively. An object is shown
0031-9120/14/030314+05$33.00
c 2014 IOP Publishing Ltd
How to see shadows in 3D
which result in less eye-crossing will be perceived
as deep (i.e. further away from the viewer) [7].
It should be noted that this stereoscopic threedimensional display can only work properly under
the condition that there is no cross-talk between
the optical information received by the two eyes.
A pair of red and cyan filters should work for this
purpose because the spectral properties of these
filters complement each other, i.e. no light coming
through the red filter can pass the cyan filter and
no light coming through the cyan filter can pass
the red filter.
It should be noted that the viewer can still
see a proper three-dimensional shadow even when
they move around. A curious student can verify
this, both experimentally by using a real set-up and
theoretically using simple schematic drawings.
Figure 1. A schematic illustration of (a) how a pair of
coloured shadows can be cast on a screen and (b) how
these coloured shadows can be displayed as stereoscopic
shadows. See the text for details.
by its two edges, i.e. A and B. A shadow with three
different colours will be cast on the screen S: a red
shadow (in regions where the object blocks the
cyan light), a black shadow (in regions where the
object blocks both the red and cyan light) and a
cyan shadow (in regions where the object blocks
the red light).
Figure 1(b) illustrates how these coloured
shadows can be displayed as stereoscopic shadows. In this example, the viewer’s eyes E1 and E2
are filtered with red and cyan filters, respectively.
Due to the red filter, the eye E1 will only perceive
the black and cyan shadows, spanning between
the points AL1 and BL1 ; it sees the red shadow
simply as bright as the screen surface (i.e. no
shadow). Meanwhile, due to the cyan filter, the eye
E2 will only perceive the black and red shadows,
spanning between the points AL2 and BL2 ; it sees
the cyan shadow simply as bright as the screen
surface (i.e. no shadow). This occurs such that the
viewer will cross their eyes: the left eye will look
at the right-hand side of the screen while the right
eye will look at the left-hand side of the screen.
The brain of the viewer then uses the information
from the muscles that move the crossing eyes to
create a three-dimensional image of the shadow:
some parts of the shadow which result in more
eye-crossing will be perceived as shallow (i.e.
closer to the viewer) and other parts of the shadow
May 2014
A simple set-up for stereoscopic shadows
In this section we describe how to build a very simple set-up for stereoscopic shadows. Figures 2(a)
and (b) show how we used a coloured light source
made using a Panasonic BF-977 LED Lamp
(Panasonic, Japan), which has three lamps in
it, with the addition of red and cyan filters
made from low-cost plastic sheets. Figure 2(c)
shows an object, along with the resulting coloured
shadows, cast on the wall behind the object. The
characters on the right side (‘I’, ‘R’, ‘1’ and ‘0’)
are positioned closer to the wall relative to the
characters on the left side (‘A’, ‘J’, ‘S’, and ‘2’).
Hence, when a red filter is positioned in front of
the viewer’s left eye and a cyan filter is positioned
in front of the viewer’s right eye, the coloured
shadows of the characters on the left side and the
right side result in higher and lower degrees of
eye-crossing, respectively. This, in turn, results in
the shadow of the characters on the left side being
perceived as closer to the viewer relative to the
shadow of the characters on the right side.
We used the image processing software
ImageJ1 to split the digital RGB image into the
red, green and blue channels (see figures 2(d)–(f)),
simulating how the shadows will be perceived
when a viewer uses a red, a green or a blue
filter, respectively. Because the cyan filter does
not perfectly balance the weighting factors of the
green and blue filters, the simulated shadow for the
green filter does not perfectly match the simulated
1
www.rsbweb.nih.gov/ij/.
PHYSICS EDUCATION
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G O F Parikesit
Figure 2. A coloured light source made from three lamps and two colour filters, (a) before and (b) after the
filters were added. The resulting coloured shadows (c) of an object were cast on the wall, along with the simulated
shadows seen with (d) a red filter, (e) a green filter and (f) a blue filter.
shadow for the blue filter. However, the simulated
shadow for the red filter is significantly different
from the simulated shadows for the green and blue
filters, indicating that we have minimal cross-talk
between the red and cyan filters in our light source.
In order to better display the shadows stereoscopically, we need to engineer the light source
so that we will only obtain two coloured shadows
(and no more than that). We therefore performed
further experiments using two Lightspro LED
Lamps (Lightspro, Indonesia) which had been
equipped with light absorbers (to block unwanted
parts in the light sources) as well as red and
cyan filters. As shown in figure 3, this experiment
results in only two shadows, which can then be
viewed stereoscopically using a pair of glasses
equipped with the corresponding colour filters.
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PHYSICS EDUCATION
Student activities
The casting of coloured shadows and stereoscopic
display of them can be a good way to raise
students’ curiosity on the optics of shadows.
However, we can further raise their curiosity
by engaging them in more activities. Here, we
describe two types of activities: mathematical
analysis and conceptual investigations.
Mathematical analysis of stereoscopic shadows can be performed by using the following
questions.
• Casting of coloured shadows: given the
coordinates of L1 , L2 , A and B, can you
determine the coordinates of the coloured
shadows’ edges AL1 , AL2 , BL1 and BL2 ?
(Hint: because light rays travel in straight
May 2014
How to see shadows in 3D
Figure 3. A better coloured light source, made using appropriate (a) light absorbers and (b) colour filters, results
in (c) a pair of coloured shadows that can be viewed stereoscopically using glasses equipped with red and cyan
filters positioned in front of the left and right eyes, respectively, such that the viewer crosses their eyes.
lines, the line that connects A and L1 will
arrive at AL1 ; the same holds for AL2 , BL1
and BL2 .)
May 2014
• Display of stereoscopic shadows: given the
coordinates E1 , E2 , AL1 , AL2 , BL1 and BL2 ,
can you determine the coordinates of the
PHYSICS EDUCATION
317
G O F Parikesit
stereoscopic shadow’s edges A0 and B0 ?
(Hint: due to the viewer’s eye-crossing, the
point A0 is formed by the intersection
between the line that connects AL2 to E2 and
the line that connects AL1 to E1 ; a similar
method holds for finding the point B0 .)
Conceptual investigations can be performed
using the following questions.
• Why do we find it more difficult to obtain
stereoscopic shadows when we use
non-point-like light sources?
• Can we still obtain stereoscopic shadows
when we swap the colours of the filters
positioned in front of the two eyes?
• What happens if the object’s dimensions are
smaller than the distance between the two
light sources?
• Can we use filters of different colours (i.e.
other than red and cyan)?
While the first type of activity, which allows
students to deepen their understanding on the
observed stereoscopic shadows, is more suitable
for high-school students, the second type of activity, which can be useful to foster critical thinking
abilities among students, is probably more suitable
for first-year undergraduate students. The conceptual investigations can be performed either theoretically using schematic drawings and mathematical
analysis or experimentally using a real set-up of
stereoscopic shadows.
Conclusions
We have described a method to raise students’
curiosity on how shadows work, particularly by
casting coloured shadows and displaying them
in 3D using a stereoscopic set-up. We have also
suggested a way to build a very simple set-up of
stereoscopic shadows, which is suitable for classroom demonstrations. Aiming to further raise the
students’ curiosity, we have also included a list of
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PHYSICS EDUCATION
student activities, which comprise a mathematical
analysis and a conceptual investigation. We foresee that our method will be able to attract more
students to learn about how light works in general
and how shadows work in particular.
Received 12 February 2014, revised 12 March 2014, accepted
for publication 14 March 2014
doi:10.1088/0031-9120/49/3/314
References
[1] Lynch D K and Livingston W 2001 Color and
Light in Nature (Cambridge: Cambridge
University Press)
[2] Chen F P 2003 Shadow theaters of the world
Asian Folklore Studies vol 62 (Nagoya: Nanzan
University) pp 25–64
[3] Foley K 2010 Dancing shadows, epic tales:
wayang kulit of Indonesia (review) Asian
Theatre J. 27 394–9
[4] McIntire J P, Havig P R and Geiselman E E 2014
Stereoscopic 3D displays and human
performance: a comprehensive review Displays
35 18–26
[5] http://cimimarie.com/christinemarie/
Christine Marie.html, (accessed on 15 February
2014)
[6] von Goethe J W 1810 Theory of Colors (London:
John Murray)
[7] Gregory R L 1964 Stereoscopic shadow-images
Nature 203 1407–8
Gea O F Parikesit joined the
Department of Engineering Physics at
the Gadjah Mada University in Indonesia
in 2009, following two years of
post-doctoral research work on
nano-particle image velocimetry at the
Delft University of Technology. He
obtained his degrees from the Delft
University of Technology in The
Netherlands (PhD in Applied Physics
with research work in the Quantitative
Imaging research group; MSc in Applied
Physics with research work in the Optics
research group) and the Bandung
Institute of Technology in Indonesia (ST
in Engineering Physics with research
work in the Optics laboratory). His
current research activities are centred on
the field of optics education.
May 2014