how to draw a ray diagram

Ray Diagrams - Concave Mirrors

The theme of this unit has been that we encounter an object considering light from the object travels to our eyes as nosotros sight along a line at the object. Similarly, we see an image of an object considering light from the object reflects off a mirror and travel to our optics as we sight at the image location of the object. From these two basic premises, we have divers the epitome location equally the location in space where light appears to diverge from. Ray diagrams accept been a valuable tool for determining the path taken by lite from the object to the mirror to our eyes. In this section of Lesson 3, we will investigate the method for drawing ray diagrams for objects placed at diverse locations in front end of a concave mirror.

To draw these diagrams, nosotros will have to recall the two rules of reflection for concave mirrors:

Any incident ray traveling parallel to the main axis on the style to the mirror volition pass through the focal point upon reflection.
Any incident ray passing through the focal signal on the way to the mirror volition travel parallel to the primary centrality upon reflection.

Earlier in this lesson, the following diagram was shown to illustrate the path of light from an object to mirror to an eye.

In this diagram five incident rays are drawn along with their corresponding reflected rays. Each ray intersects at the paradigm location and and so diverges to the eye of an observer. Every observer would detect the same image location and every light ray would follow the police force of reflection. Withal simply two of these rays would be needed to determine the paradigm location since it simply requires two rays to find the intersection point. Of the five incident rays fatigued, 2 of them correspond to the incident rays described by our two rules of reflection for concave mirrors. Because they are the easiest and most predictable pair of rays to describe, these will be the two rays used through the remainder of this lesson.

Footstep-by-Step Method for Drawing Ray Diagrams

The method for cartoon ray diagrams for concave mirror is described below. The method is applied to the task of drawing a ray diagram for an object located beyond the middle of curvature (C) of a concave mirror. Yet the same method works for drawing a ray diagram for any object location.

i. Pick a point on the elevation of the object and describe two incident rays traveling towards the mirror.

Using a straight border, accurately draw ane ray so that it passes exactly through the focal point on the manner to the mirror. Draw the second ray such that information technology travels exactly parallel to the principal axis. Identify arrowheads upon the rays to indicate their direction of travel.

2. Once these incident rays strike the mirror, reflect them according to the 2 rules of reflection for concave mirrors.

The ray that passes through the focal signal on the style to the mirror will reflect and travel parallel to the primary centrality. Use a directly edge to accurately describe its path. The ray that traveled parallel to the principal axis on the way to the mirror will reflect and travel through the focal bespeak. Identify arrowheads upon the rays to point their direction of travel. Extend the rays past their point of intersection.

three. Mark the epitome of the top of the object.

The image point of the top of the object is the point where the two reflected rays intersect. If your were to draw a 3rd pair of incident and reflected rays, then the third reflected ray would besides pass through this point. This is simply the betoken where all calorie-free from the elevation of the object would intersect upon reflecting off the mirror. Of course, the residual of the object has an epitome also and it can be found by applying the same three steps to another chosen bespeak. (See note below.)

4. Repeat the process for the bottom of the object.

The goal of a ray diagram is to decide the location, size, orientation, and blazon of image that is formed by the concave mirror. Typically, this requires determining where the prototype of the upper and lower extreme of the object is located and and then tracing the unabridged image. After completing the showtime three steps, merely the image location of the top extreme of the object has been institute. Thus, the process must be repeated for the signal on the lesser of the object. If the bottom of the object lies upon the principal axis (as it does in this example), then the image of this point will also lie upon the primary axis and exist the aforementioned distance from the mirror as the image of the superlative of the object. At this betoken the unabridged image can exist filled in.

Some students have difficulty agreement how the entire paradigm of an object tin exist deduced in one case a single signal on the prototype has been determined. If the object is a vertically aligned object (such equally the arrow object used in the example below), so the procedure is easy. The epitome is merely a vertical line. In theory, it would be necessary to pick each signal on the object and draw a split up ray diagram to determine the location of the paradigm of that point. That would require a lot of ray diagrams as illustrated below.

Fortunately, a shortcut exists. If the object is a vertical line, so the prototype is too a vertical line. For our purposes, we will only deal with the simpler situations in which the object is a vertical line that has its bottom located upon the primary axis. For such simplified situations, the paradigm is a vertical line with the lower extremity located upon the master axis.

The ray diagram above illustrates that when the object is located at a position beyond the center of curvature, the paradigm is located at a position betwixt the center of curvature and the focal point. Furthermore, the image is inverted, reduced in size (smaller than the object), and real. This is the blazon of information that nosotros wish to obtain from a ray diagram. These characteristics of the image will exist discussed in more detail in the next section of Lesson 3.

Once the method of drawing ray diagrams is practiced a couple of times, it becomes as natural as breathing. Each diagram yields specific information about the image. The two diagrams below evidence how to determine image location, size, orientation and type for situations in which the object is located at the heart of curvature and when the object is located between the center of curvature and the focal bespeak.

It should be noted that the procedure of amalgam a ray diagram is the aforementioned regardless of where the object is located. While the consequence of the ray diagram (epitome location, size, orientation, and type) is different, the same 2 rays are e'er drawn. The ii rules of reflection are applied in order to determine the location where all reflected rays appear to diverge from (which for existent images, is also the location where the reflected rays intersect).

In the 3 cases described above - the example of the object being located beyond C, the case of the object being located at C, and the case of the object being located between C and F - light rays are converging to a point later reflecting off the mirror. In such cases, a existent image is formed. As discussed previously, a real image is formed whenever reflected light passes through the image location. While plane mirrors ever produce virtual images, concave mirrors are capable of producing both real and virtual images. As shown above, real images are produced when the object is located a distance greater than ane focal length from the mirror. A virtual image is formed if the object is located less than one focal length from the concave mirror. To see why this is then, a ray diagram tin be used.

Watch It!

A physics instructor discusses the nature of a existent image using a phun physics sit-in.

Ray Diagram for the Formation of a Virtual Image

A ray diagram for the case in which the object is located in forepart of the focal betoken is shown in the diagram at the right. Observe that in this case the light rays diverge afterwards reflecting off the mirror. When light rays diverge after reflection, a virtual image is formed. As was done with airplane mirrors, the paradigm location can exist found by tracing all reflected rays backwards until they intersect. For every observer, the reflected rays would seem to be diverging from this point. Thus, the point of intersection of the extended reflected rays is the prototype point. Since light does not really pass through this point (light never travels behind the mirror), the image is referred to equally a virtual paradigm. Observe that when the object in located in front of the focal point, its image is an upright and enlarged epitome that is located on the other side of the mirror. In fact, one generalization that tin can be made most all virtual images produced by mirrors (both plane and curved) is that they are always upright and always located on the other side of the mirror.

Ray Diagram for an Object Located at the Focal Point

Thus far we accept seen via ray diagrams that a existent image is produced when an object is located more than one focal length from a concave mirror; and a virtual prototype is formed when an object is located less than one focal length from a concave mirror (i.e., in front of F). But what happens when the object is located at F? That is, what type of prototype is formed when the object is located exactly 1 focal length from a concave mirror? Of form a ray diagram is always ane tool to aid notice the answer to such a question. However, when a ray diagram is used for this case, an immediate difficulty is encountered. The incident ray that begins from the summit extremity of the object and passes through the focal bespeak does not meet the mirror. Thus, a different incident ray must exist used in order to determine the intersection point of all reflected rays. Whatever incident lite ray would work every bit long equally it meets up with the mirror. Recall that the simply reason that we take used the two we take is that they can be conveniently and hands drawn. The diagram beneath shows two incident rays and their corresponding reflected rays.

For the example of the object located at the focal signal (F), the light rays neither converge nor diverge after reflecting off the mirror. As shown in the diagram above, the reflected rays are traveling parallel to each other. Subsequently, the light rays will not converge on the object's side of the mirror to form a existent image; nor can they be extended backwards on the contrary side of the mirror to intersect to form a virtual prototype. So how should the results of the ray diagram be interpreted? The answer: there is no image!! Surprisingly, when the object is located at the focal betoken, at that place is no location in infinite at which an observer tin can sight from which all the reflected rays appear to be diverging. An paradigm is not formed when the object is located at the focal point of a concave mirror.

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Cheque Your Understanding

The diagram below shows two light rays emanating from the height of the object and incident towards the mirror. Describe how the reflected rays for these light rays tin can be drawn without actually using a protractor and the law of reflection.