Shrinking Heads and Sharper Sundials

Last updated on September 16, 2023

Shrinking Heads and Sharper Sundials: Unveiling the Secrets of Strange Shadows

Have you ever noticed that shadows can sometimes behave in peculiar ways? Andrew Kirk, an avid observer of atmospheric phenomena, stumbled upon a fascinating phenomenon one morning while out for a jog. He noticed that the shadow of his head appeared to shrink whenever it passed over the shadow of a utility pole. Intrigued by this peculiar observation, he decided to document it and returned the next day to further investigate. Little did he know that this simple observation would lead him to uncover the intriguing secrets behind shrinking heads and sharper sundials.

The Mystery Unveiled: Understanding the Changes in Shadow Width

As Andrew continued his observations, he noticed an interesting pattern. While the width across his shoulders remained constant, the width of his head's shadow underwent a significant change. This raised two fundamental questions:

1. Why does the width of the head's shadow change?
2. Why is the narrow head shadow much sharper than the normal one on the right?

The easy explanation lies in our proximity to the sun. Being close enough to see the sun as a disk plays a crucial role in these optical phenomena. However, understanding the "how" requires a deeper exploration.

The Anatomy of Shadows: Umbra and Penumbra

To comprehend the behavior of shadows, we must first understand the concept of umbra and penumbra. When we observe the head shadow away from the pole, we notice that the sun's disk has a diameter of approximately 0.5° and its rays diverge slightly from parallel. This divergence creates a volume of darkness known as the umbra, where no sunlight can reach. As we move farther away from the head, the umbra gradually narrows. Beyond the umbra lies the penumbra, where only part of the sun is obscured, resulting in a less intense shadow with a broad fuzzy edge.

Similarly, the shadow cast by the utility pole exhibits a similar pattern. It consists of a central dark umbra, unlit by direct sunlight, surrounded by a penumbra of graded intensity. The disks on the left side of the figure illustrate the appearance of the sun at different points within the penumbra. As we move closer to the shadow's centerline, the pole progressively blocks more and more of the sun, leading to an eclipse-like effect.

Unveiling the Sharper Shadow: The Role of Second Shadows

The real intrigue begins when the head forms a second shadow within the broad shadow zone of the pole. If we closely examine the upper edge of the head in the figure, we notice that the sun is almost blocked by the pole. Only rays traveling in a specific direction, let's call it "A," from the unobscured edge of the sun, are available to define the edge of this second shadow. In contrast, rays in direction "B" are blocked by the pole, resulting in an absence of rays and, subsequently, a lack of penumbra. Consequently, this second shadow exhibits sharp and dark edges, which further enhance its narrowness compared to the standalone shadow.

The Shadow Sharpener: A Sundial's Secret Weapon

This intriguing optical phenomenon not only provides a fascinating insight into the behavior of shadows but also has practical applications. By experimenting with a pencil in and out of the shadow cast by a strip of opaque tape on a window, we can observe the same geometry at play. Additionally, using a large pinhole in a card placed inside a shadow can serve as a basis for a shadow sharpener. This innovative technique can enhance the accuracy of reading time on a sundial.

Embracing the Optical Wonders Around Us

Andrew Kirk's serendipitous observation highlights the subtle yet captivating optical effects that surround us daily. By paying attention to the world around us, we can uncover the hidden secrets of atmospheric optics. Shadows, often taken for granted, can reveal intriguing phenomena that spark our curiosity and deepen our understanding of the natural world.

So, the next time you encounter a peculiar shadow, take a moment to appreciate the intricate play of light and darkness. Who knows what mysteries may unfold before your eyes?

Shrinking Heads & Sharper Sundials

Strangely behaving shadows captured by Andrew Kirk.

"It was shortly after sunrise. Shadows were very long with distinct penumbras. As I jogged along, I noticed the shadow of my head shrink each time my shadow passed over the shadow of a utility pole. So I stopped to document it, and returned next day, too."

"The pole was ~35 mm diameter at chest height. While photographing I

stood about 25 meters away from it."

The width across the shoulders of Andrew's shadow stays the same. (1) Why does the width of the head change? (2) Why is the narrow head shadow much sharper than the normal one on the right?

'Because we are close enough to the sun to see it as a disk' is the easy explanation. The 'how' takes longer!

Look at the head shadow away from the pole. The sun's disk is 0.5° in diameter and its rays diverge from parallel by that amount. There is a volume of darkness extending from the head in which no sunlight can reach - this is the umbra. The umbra narrows farther from the head. Outside of the umbra only part of the sun is obscured and the shadow is less intense - this is the penumbra.

The resulting shadow on a wall or the ground has a dark core (umbra) narrower than the object casting it and a broad fuzzy edge (penumbra).

The pole shadow is similar. There is a narrowing dark central umbra unlit by any direct sunlight surrounded by a penumbra of graded intensity. The disks at left show the sun's appearance at different points inside the penumbra. Closer to the shadow centerline the pole cuts off - eclipses - more and more of the sun.

The fun starts when the head forms a second shadow inside the broad pole shadow zone. Look at the upper edge of the head in the figure at left. The sun is almost blocked by the pole. Only rays traveling in the direction 'A' from the unobscured edge of the sun are available to define the edge of the second shadow. There are no rays in direction B because they are blocked by the pole. The result - There is a sharp and dark shadow edge formed by rays like A and there is almost no penumbra.

The penumbra-less shadow is therefore narrower than the stand alone shadow and its sharp edges perhaps enhance the narrowness.

Experiment with a pencil in and out of the shadow of a strip of opaque tape pasted on a window. The geometry is the same. Then try a large pinhole in a card inside a shadow - that is the basis of a shadow sharpener to tell the time on a sundial better! Subtle optical effects like this are all around us.

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