When the sun is at the top of the head then the length of the shadow of a man will be

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When children draw pictures of the Sun, they often show rays radiating outwards – similar to the image below.

These light rays travel in a straight line at nearly 300,000 kilometres per second. Sunlight that travels towards the Earth takes just over 8 minutes to reach us. When the rays reach Earth, they hit whatever is in their path. If the object they hit is opaque, the light cannot pass through, and a shadow forms.

Simply speaking, a shadow is an absence of light. If light cannot get through an object, the surface on the other side of that object (for example, the ground or a wall) will have less light reaching it.

A shadow is not a reflection, even though it is often the same shape as the object.

Light sources and shadows

There are many sources of light – stars like our Sun, candle flames, light bulbs, glow-worms and computer screens produce light. All of this light travels in a straight line until it hits something. Sometimes, it travels a short distance – like when we switch on the lamp. Other times, light travels thousands of years – like the light from stars we see in the Milky Way.

It is easy to see our shadows when we are outdoors in the sunshine on a clear, bright sunny day, but do shadows form when an object blocks light from other sources? The answer is yes, but they may be difficult to see if the light source is not very bright (has a low light intensity). Shadows are also more definite (sharper) where there is contrast between the shadow and the lit surface, for example, a shadow on a white wall will be more easily seen.

The size of the light source can sharpen or blur the shadow. A small spotlight like a cellphone torch forms a more distinct shadow than an overhead room light, but the sharpness of the shadow changes when the torch moves away from the object.

Changing shapes and sizes

A shape of an object always determines the shape of its shadow. However, the size and shape of the shadow can change. These changes are caused by the position of the light source.

When we are outside on a sunny day, we can see how our shadows change throughout the day. The Sun’s position in the sky affects the length of the shadow. When the Sun is low on the horizon, the shadows are long. When the Sun is high in the sky, the shadows are much shorter. We can create the same effects indoors by changing the position of a torch as it shines on an object.

Although the shadow effects are the same, the reasons for the moving light source are very different. When we use a torch to make long and short shadows indoors, it is the light source that moves. When the Sun makes long and short shadows outdoors, it is the Earth, not the light source (Sun), that moves.

The spinning Earth

From our vantage point on Earth, it appears that the Sun moves across the sky during the day. We see the Sun appear to rise in the east and set in the west. Actually, the Earth is spinning (rotating on its axis) so it is our view of the Sun in the sky that changes during each 24-hour cycle of light and dark.

We see the sunrise when our location on Earth spins towards the light of the Sun. As the Earth continues to spin, we see the Sun higher in the sky. As the Earth spins away from the light, we see the sunset. The Earth continues to spin until we are in a shadow – our place on Earth is dark because the Sun’s light is blocked by the magnitude of our planet! We have several hours of night with our side of the Earth in darkness, and then as the Earth spins towards the Sun’s light, we see a sunrise. When New Zealand is in darkness during the night, the opposite side of the world is in sunlight.

Shadows change with the seasons

The tilt of the Earth’s axis affects the length of our shadows. During the summer, our location is tilted towards the Sun, so our midday shadows are very short. During the winter, our location is tilted away from the Sun, so our midday shadows are longer.

Wikimedia Commons has images of shadows in many different settings and contexts. They are ideal for eliciting student understanding about shadows and generating discussion.

The crispest shadows are those made by the sun. The higher the sun is in the sky, the shorter are the shadows produced. In the same way, the lower the sun, the longer are the shadows. When the sun is halfway between the horizon and the top of the sky, the shadows are the same length as the object causing the shadow. This halfway height corresponds to the sun’s altitude being 45 degrees. On March 7-8, the sun peaks at a 45 degree angle. In mid day (about 12:25 p.m.) on those dates, your shadow will be as long as your height. At the start of summer (around June 21), we have our shortest shadows in mid day (about 1:15 p.m.). Your shadow then will be only 31.5 percent as long as your height. When the sun appears low in the sky, your shadow can be huge. The length of shadow to your height is proportional to 1/Tangent (sun’s altitude). If the sun is low in the sky (10 degrees), your shadow would be 5.67 times as long as your height. The corresponding ratio at 5 degrees is 11.43 . (So an average height person (5.8 feet) would have a 66 foot long shadow). When the center of the sun is 1 degree above the horizon, your shadow would be 57.3 as long as your height, making an average person’s shadow longer than the spacing between goal lines on a football field. To find the length of shadows of planets or moons in space (where these bodies block out the sun’s light), we need to know the radius of the sun, the radius of the moon or planet and the distance between the sun and the planet or moon. The length of the shadow in space can be found by using the equation of a straight line, often stated as Y = Slope*X + Intercept (value of Y for X = 0) . For the Earth at its average distance from the sun, Earth’s shadow extends 847,000 miles from its center. At our moon’s average distance from the Earth, our shadow is nearly 5,700 miles wide, 2.7 times as wide as the moon. So we can have lunar eclipses where the moon appears deep within the Earth’s shadow that can last for hours. The moon’s average shadow length is 227,000 miles, somewhat smaller than our moon’s average distance of 239,000 miles. So during a typical solar eclipse, the moon’s shadow doesn’t quite reach to the Earth’s surface; earth observers underneath the shadow would see the moon only covering up the central part of the sun (an annular or ring-like eclipse). When the moon’s distance to our Earth’s surface is closer than its shadow length, we can have a total solar eclipse lasting typically several minutes. The next good solar eclipse in North America will be on August 21, 2017. Applying the same methods, the planet Jupiter at its average distance from the sun has a 54.5 million mile shadow. Saturn at nearly twice the distance from the sun and nearly the same size as Jupiter has a shadow nearly twice as long. This shadow is comparable to Neptune’s shadow. Neptune is about 3.9 times the size of the Earth and averages 30 times as far from the sun as Earth. Neptune’s average shadow length is 103 million miles, more than the Earth-sun distance. Wednesday evening’s lunar eclipse Early in the evening this Wednesday, you will see a bright full moon among the stars of Leo. Very close to the moon will be the star Regulus, the heart star of Leo. To the left of the moon will be the planet Saturn, shining with a steady light. About 8:45 p.m., you will notice a darkening of the left side of the moon. By 10 p.m., the moon will be entirely within the Earth’s shadow. The moon will likely look dark gray, receiving only light bent around the edge of the Earth. At 10:26 p.m., the moon will be deepest in the Earth’s shadow and darkest. Then at 10:52 p.m., the moon will start to emerge from the Earth’s shadow; the same side that darkened first will be the first area to lighten. About 12:09 a.m. (the next morning), the moon will be free of the Earth’s deep shadow. The next lunar eclipse visible from this area will be about two years from now. So hope for clear weather this Wednesday. Continuing at the Frostburg State University is “Calendars Around the World” with free public presentations at 4 p.m. and 7 p.m. this Sunday and next Sunday. The Planetarium is just off the front lobby of Tawes Hall (Room 302). Tawes Hall is between the Compton Science Center and the Lane University Center. Tawes Hall is also between the Performing Arts Center and Dunkle Hall. Following our Planetarium programs, there are tours of the Compton Exploratorium, featuring an extraordinary display of mammals, the Cavallaro Collection. All these presentations are free.

Bob invites any reader comments or questions; his email is .