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Light is one of the cornerstones of physics. By understanding how light behaves, we have been able to create tools that change the way it travels. Some examples include mirrors and lenses, which we combine to make telescopes for studying distant stars or microscopes to observe life at the microscopic level. We can understand how mirrors and lenses work using ray diagrams. These diagrams show us how light behaves, the path it follows, and how it forms the images we see. Let's have a more detailed look at ray diagrams and some of their applications.
In physics, ray diagrams are a visual representation of the propagation of light. They can help us to understand and visualise multiple situations, such as light being reflected off of a mirror or changing its direction while moving through a lens.
A ray diagram is a simplified representation of light to study the trajectory that it follows as it moves from one point to another. In these diagrams, the initial point often represents the source location while the ending point represents the observer's position.
You can think of a ray diagram as a hand-drawn simulation of how light will move to predict where it will end, and how it will form the images we see and their characteristics. Each ray represents a beam of light and they are drawn following certain rules that depend on the geometry and properties of the object that the ray encounters on its way. This may sound complicated but is actually a very practical way to simplify the study of light. A deep understanding of how light interacts with different surfaces and materials is very complex and depends on many variables. With a ray diagram we can focus our attention on the essential details simplifying the study of light rays.
But why do we actually use ray diagrams if they are an oversimplification of how light works? It is fair to admit that we are leaving many details out when we use ray diagrams. However, by abstracting ourselves from the complex picture and leaving aside unnecessary details - for example, how much light is absorbed in mirror and how much is reflected, the material of a lens, how many times and at which points does light actually changes direction in a lens - we can focus on the fundamental elements that are truly necessary to predict the behaviour of light in very specific cases. As simple as they are, rays diagrams can be applied to describe correctly multiple situations: differently shaped mirrors, diverging and converging lenses, and even compound lens systems like microscopes and telescopes.
Ray diagrams can sometimes also be called light ray diagrams. Don't worry if you see a question asking you about one or the other, they mean the same thing! Light ray diagrams will always follow some basic rules, no matter if the diagram is for a pinhole camera, a mirror, or a convex lens:
Since ray diagram can represent multiple situations, more rules are applied depending on the specific case. Let's explore an example of a ray diagram for a plane mirror, so that you can see what a ray diagram looks like.
The diagram below is a ray diagram showcasing the reflection of light in a plane mirror.
This ray diagram of a plane mirror shows how light rays reflect with a reflecting angle equal to the angle of incidence. StudySmarter Originals
The first orange line represents the light ray travelling from the light source towards the mirror. Note that as light travels through the same medium it follows a straight line, so make sure you always use a ruler to draw the light rays! This ray diagram is one of the simplest, as it only involves one ray. When we start to look at ray diagrams of lenses, we will need to draw multiple rays, but more on that later.
There is one main rule to draw the ray diagram of a mirror: when light reflects, the angle of incidence is always equal to the angle of reflection.
In the diagram above, the angle of incidence is marked as
and the angle of reflection is marked as
. To identify them we first draw a normal line.
The normal line is an imaginary line that extends perpendicular to the surface of the mirror, from the point where the light ray is incident to it.
The angle of incidence is the angle formed between the incident ray and the normal.
The angle of reflection is the angle between the reflected ray and the normal.
We've looked at a regular plane mirror. Let's now consider a particular array of mirrors that can be extremely useful: an L-shaped mirror. Below is a diagram for an L-shaped mirror:
The ray diagram for an L-shaped shows how a ray is reflected back, parallel to the incident ray. StudySmarter Originals
Notice that there are two locations where reflection occurs. This causes the ray of light from the source to be reflected back in the same direction the ray had when it was incoming. This phenomenon is called retroreflection and it work regardless of the angle of incidence. Moreover, we can scale up this set up by adding a third mirror perpendicular to these two. The result is a mirror with the shape of the corner of a cube. In this three dimensional array any light ray is always reflected directly back to its source.
Did you know that in 1969 as part of the Apollo 11 moon mission, astronauts were asked to leave a panel with retroreflectors? This was done so that we could aim a laser from the earth at them and guarantee that light would bounce exactly back in the same direction. Some of the most precise measurements of the distance between the moon and the earth we have to this day were obtained with this method. This is a very impactful experiment and it can be understood with a relatively simple ray diagram!
A panel with retroreflectors was deploy to reflect a laser beam back to its source on earth. NASA
A lens is any shaped piece of material that refracts light in a specific way.
Usually, lenses are made from glass, but they can also be made from any transparent material, for example, plastic or even ice! As a quick recap, lenses are a type of object that refracts light, but what does that mean?
Refraction is the process where light changes direction when it enters or leaves a new medium, and it takes place because light has a different speed in those mediums.
When the light goes through a water-air interface, it changes its direction. This is why an object looks like it is bent when it is partially submerged in a glass of water. The light coming from the submerged part seems to come from a different position than it really is.
A pen appears to be bent or broken when partially submerged in water, Kunal B Mehta CC BY-SA 4.0
As parallel light rays propagating through the air enter a convex lens they get refracted coming together at a single point.
A convex lens is a lens that is thicker in the middle than at the edges and concentrates light rays at a single point called the principal focus. This is why convex lenses are also called converging lenses.
For a regular convex lens, the principal focus will always be along the principal axis.
The principal axis is an imaginary horizontal line that goes through the geometric centre of a lens.
Light rays parallel to the principal axis converge at the focus after being refracted by the convex less, StudySmarter Originals
Notice that the light refracts twice. The first time the light refracts is when it moves from the air into the lens, and then once again as they leave the lens. This is not a ray diagram, when we draw ray diagrams we consider that light rays will only refract at one point, and as such, we can use a much simpler representation for a converging lens. See below for the ray diagram for a convex lens.
In a ray diagram, a convex lens is represented as a vertical line segment with two arrows pointing upwards in the extremes, StudySmarter Originals
In this ray diagram, notice that we have labelled both of the foci as
and
to allow us to distinguish between each of them. Convex lenses can work in either direction, so if you had a series of parallel light rays hitting the lens from the right-hand side they would come together at the focus on the left-hand side.
Instead of analysing how each light ray will refract, we can get a good understanding of the behaviour of the light rays that go through a convex lens by using the following three special cases:
A light ray parallel to the principal axis, a ray passing through the centre of the lens, and a ray passing through the focus are special cases that refract in a predictable manner. StudySmarter Originals
Besides convex lenses, the other main type of lens that you need to be familiar with is the concave lens.
A concave lens is a diverging lens that causes light rays that are parallel to the principal axis to disperse after they have been refracted by the lens. These rays spread out in such a way that makes them look like they are emerging from a single point called the principal focus of the lens.
You can generally tell if a lens is concave because it is rounded inwards, like a shallow cave in the glass! The following diagram illustrates how light rays passing through a concave lens are dispersed.
A concave lens makes the light rays diverge, StudySmarter Originals
As with a convex lens, the light refracts twice, once when entering the lens and once when leaving the lens. However, we can simplify this and create a ray diagram like the one below, which represents the same situation as the image above.
A concave lens is represented by a vertical line segments with two arrow head point inwards on its ends. StudySmarter Originals
In this ray diagram, notice that the lens is represented by a vertical line segment with two arrowheads pointing inwards.
Similarly to the case of concave lenses, we can simplify the interaction of the light with a concave lens by using the following three special cases:
In the diagram for a concave lens, light rays passing through the centre do not change direction, but a ray parallel to the principal axis refracts as it came from the focus. StudySmarter Originals
If you would like to see a more in-depth explanation of ray diagrams to study how images form, and how lenses can magnify images and correct eyesight problems you can take a look at the article on image formation with lenses.
A ray diagram is a simplified representation of the light that shows the trajectory ray of light from an object to a viewer and shows illustrates how light it interacts with the objects that it may encounter on its way, like mirrors or lenses.
A ray diagram must be drawn with a ruler, as all of the rays of light must be straight lines. This is because light only travels in straight lines. Also, an arrow on the tip of the ray shows the direction of propagation of light. More specific rules depend on whether the light will interact with a mirror or a lense, and their type.
We can distinguish two main important diagrams for concave mirrors:
1. When the object is located farther than the focus of the concave, the image is real, inverted, and reduced in size.
2. When the object is located before the focus of a concave mirror, the image is virtual, upright, and enlarged.
One of the best examples of applications of ray diagrams is how they can describe image formation by lenses. This allows us to understand how a magnifying glass works.
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