The shadow is formed by the obstruction of light. Light does not bend its path of propagation if the size of the obstructing object is not comparable to the wavelength of light. Therefore, the shadow of the object formed as a dark (light-less) image because of obstruction of light paths by an object.
Index of Article
- What is a shadow?
- How is shadow formed?
- Size and Shape of a Shadow
- Different parts of shadow
- What is an umbra?
- What is a penumbra?
- What is a antumbra?
- How shadow changes with variation in daytime?
- What is the color of shadows?
- How come there are still shadows in the dark?
- Propagation speed of a shadow
- Shadow inversions
- What is a rain shadow?
- Numerical on shadows
A shadow refers to a dark real silhouette of a person or an opaque object that is generated when the object or person obstructs the light coming from a light source. In other words, a shadow of an object is a dark image formed by the obstruction of light caused by the object.
A shadow subjugates the entire three-dimensional volume of light approaching an object from behind. A shadow is the cross section of that volume of light in the form of a two-dimensional silhouette, or an inverse projection of the person or the object obstructing the propagation of light in space.
How is shadow formed?
We know that light propagates in a straight line i.e. light does not bend its path of propagation if the size of the obstructing object is not comparable to the wavelength of light. Therefore, when an object stands in the path of light, it obstructs the light rays from propagating. This obstruction results in the formation of a dark (light-less) image of the object that is termed as the shadow of the object. The object is required to be opaque for shadow formation to take place.
The size and shape of the shadow of an object can depend on a number of factors. Contrary to popular belief, the shadow is not entirely dependent on the size and the shape of the object.
Some factors on which the size and shape of a shadow depend on are:
- Angle of the propagating light beam: The angle at which the shadow falls on the is one of the most important factors in determine the shape and size of the shadow of an object. When the light falls normally or orthogonally, the shadows formed have a shorter length. When the angle between light beam and the object increases then the shadow gets elongated.
- Seasons: Seasons and weather plays a very important role in determining the shape, size, and sharpness of a shadow. In summers, during a bright sunny day the shadows formed are sharper, and the shadows stay for a longer duration of time. If the weather is cloudy, then we can see faint or no shadow formation i.e. the sharpness of the shadow is less. In winters, the shadows are formed for a lesser duration of time.
- Positioning of the light source: The shape and size of an object’s shadow is affected by the positioning of the light source. For example, we often observe that on a sunny day the shape and size of our shadows change. This happens because the positioning of the sun changes throughout the day as it appears to move from east to west. When the sun is positioned near the horizon, the shadows formed are longer in terms of length. When the sun is positioned overhead high in the sky, the shadows formed have a shorter length. This effect of the Sun’s position on shadow formation can be replicated by artificially designed moving lights. However, there is a difference between both the approaches. In case of sunlight, it is the Earth that moves while the Sun remains fixed. But in the case of a light source, the source is made to move while the object remains stationary in its position.
- The object: Primary boundary of the shape of the shadow is determined by the object blocking the light. For example, if the object is a ball, the shadow will be circular or oval. A rectangular or square shadow will be formed in case the object is a book, or a box. For humans, the shadow forms according to the actual shape of the particular being.
- Distance between the object and the surface of projection: With the increase in distance between the object and the surface of projection the size of the shadow or the silhouette increases. Therefore, it can be said that the two factors are proportional. When the object moves, it’s shadow is likely to expand in terms of dimensions faster than the speed of the object’s movements.
- Type of light source: The type of light source (big, medium, or small) determines the sharpness of the shadow formed. If the source of light is huge like the sun, then the shadow boundary is quite sharp. This sharpness reduces as we move from sunlight to a tubelight. In case the source of light is a small torch or cell phone then the shadows formed is blurry.
Frequently asked Questions related to shadow formation
What are the different parts of shadow ?
Parts of a shadow
Let us have a look at the three parts of a shadow.
What is an umbra?
The word “umbra” comes from the Latin word for “shadow”. Umbra refers to the innermost region of the shadow that appears to be the darkest. In other words, an umbra represents the part of the shadow where the light gets entirely obstructed by the blocking body. If the observer is located within an umbra, then the observer is likely to perceive a total eclipse.
For a round body that obstructs around source of light, the umbra formed has the shape of a right circular cone. If we try to view the object and the source from the apex of the cone, then the two bodies would seem to be of the same size. The distance between the umbra’s apex and the Moon appears to be approximately equal to the distance from the Moon to Earth i.e. about 384,402 km or 238,856 mi. The diameter of the Earth is about 3.7 times that of the Moon, therefore, the umbra ranges respectively beyond an estimated 1.4 million km or 870,000 mi.
What is a penumbra?
The word penumbra originated from the Latin word “paene” which means “almost or nearly”. The penumbra is a portion of the shadow of an object where only a certain part of the beam of light gets obstructed by the occluding body. An observer located in the penumbra region sees only a partial eclipse. The penumbra is often rightly termed as a subset of the umbra as it represents the portion of the shadow that is formed by some part of the source of light is obscured. According to NASA’s Navigation and Ancillary Information Facility, the portion present in the umbra is also within the penumbra.
What is an antumbra?
The word “antumbra” originated from Latin word “ante” which means “before”. The antumbra refers to the portion of the shadow from which the obstructing object appears to be placed completely within the central region of the light source. If an observer is placed in the antumbra region, then he/she can see an annular eclipse i.e. a bright ring of light enclosing the eclipsing body. With the reduction in distance between the observer and the light source, the relative size of the obstructing body increases till the time it forms a full umbra.
How shadow changes with variation in daytime?
- The shape and size of an object’s shadow is affected by the positioning of the light source. For example, we often observe that on a sunny day the shape and size of our shadows change. This happens because the positioning of the sun changes throughout the day as it appears to move from east to west. The shadow’s actual length on the ground is proportional to the cotangent of the elevation angle of the Sun (θ) with respect to the horizon.
- During sunset and sunset when the angle of elevation θ is equal to almost 0° and therefore the cotangent of the elevation angle(θ) becomes equal to ∞. As the length of the shadow is directly proportional to the cotangent of the elevation angle, we can say that in this case the shadows are very long. When the sun is located directly overhead i.e. the sunlight falls normally or orthogonally on the object (this is possible only in the region between the Tropic of Capricorn and Tropic of Cancer), then the angle of elevation becomes equal to 90°, and cot(θ) = 0. In this case, the shadows formed are smaller in length and are cast directly underneath the objects mostly.
- This property of shadows has proved out to be very useful for long aided travelers. Especially when travelling through barren regions such as the deserts, sea route, etc.
What is the color of shadows?
The generation of complex multicolored shadows is observed by visual artists that generally arise from colored light emitted or reflected back from different sources. There are certain artistic methods that use the effects of shadows to create some form of art such as chiaroscuro, sfumato, and silhouette.
We can often observe that during daytime, a shadow of an opaque object illuminated by sunlight appears to have a bluish shade. The main reason behind this is due to the Rayleigh scattering. The sky appears to be blue in color due to the same property. The opaque obstructing object is capable of blocking the light coming from sun. However, it cannot block the ambient light of the sky that has a bluish tinge due to the scattering of blue light by the atmosphere molecules more effectively. This is the reason why shadows appear to be blue.
How come there are still shadows in the dark?
- We can observe the appearance of shadows in the dark because the is light present in what we perceive as dark. Darkness is rather subjective. Even during the night time which we perceive to be dark there is light from various sources like stars, the moon, street lights, and ambient city lights reflecting off clouds, etc. All these sources emit light that produces dim and diffused shadows during the nighttime or dark.
- A shadow can be said to be a spot on a surface where the amount of light is less compared to the amount of light the area surrounding that spot. In bright light this difference is more pronounced i.e. the contrast between the shadow and the surrounding area is much more and therefore, we can clearly see the shadow formation.
What is the propagation speed of a shadow ?
- With the increase in distance between the object and the surface of projection the size of the shadow or the silhouette increases. Therefore, it can be said that the two factors are proportional. When the object moves, it’s shadow is likely to expand in terms of dimensions faster than the speed of the object’s movements.
- The increase of size and movement is also true if the distance between the object of interference and the light source are closer. However, it is wrong to say that the shadow of an object can travel in a speed faster than the speed of light even if the distance between the object and the surface of projection is large (like light years). The light loss that is responsible for projecting the shadow can travel towards the projection surface at the speed of light.
- Even though we perceive the shadow’s edge to travel along a wall, in reality the increase in the length of a shadow is due to a new projection that travels at a speed equal to the speed of light from the interfering object. It is to be noted that the communication between different points in a shadow does not exist except for the phenomenon of reflection or interference of light which occurs at the speed of light. A shadow, which is projected over an area at large distances (like light years) is unable to communicate information between the surfaces at such distances with the edge of the shadow.
What is Shadow inversions ?
We can often observe that the shadows of objects such as chain-linked fences and other objects having similar shapes tend to get inverted i.e. a swap occurs between the light and dark areas when the object gets farther from the surface of the projection. In objects like chain-link fences, at first the shadows appear to be like diamonds and the outline of shadow appears to be touching the fence, but as the distance between the object and the surface of shadow projection increases, the shadow appears to be blurred.
Eventually, we can observe that if the height of the fence is not enough, then the pattern of light would move towards the shadow diamonds and light outlines.
What is a rain shadow?
The term rain shadow is used to describe the place with the dominant wind direction, elevation and other factors that keeps the area dry.
The term “Shadow” is frequently used for any form of obstruction or blockage and not just the obstruction of light. The term rain shadow is also used in such a context. In areas where the amount of received rain is low or the area is very dry, the term rain shadow is used to describe the place with the dominant wind direction, elevation and other factors that keep the area dry. It basically describes the scarcity of rain in an area. A similar use of the term shadow is seen in acoustics. An “acoustic shadow” refers to a space or area where the propagation of direct sound is occluded or blocked or diverted to another area.
Numerical on shadows
Q. A 6ft tall man casts a shadow having a length of 12ft. What would be the length of the shadow of an 8ft tree place in the same surface as that of the man.
Ans. Since the man and the tree is on the same surface they must be facing the same elevation angle from the light source. As we know, the length of the shadow is proportional to the cotangent of the angle of elevation, we can say that
Cot(θ) = 12/6 = L/8
Or, L = 16ft
Q. A building having the height of 20m casts a shadow on the ground. If the angle of elevation of the sun is 53°, find the length of the shadow.
Ans. As we know, the length of the shadow is proportional to the cotangent of the angle of elevation, we can say that
Cot(θ) = L/20m
Or, ¾ = L/20
Or, L = 15m