Review on Ray Tracing for a Concave Mirror

Ray Diagrams - Concave Mirrors

The theme of this unit has been that nosotros see an object because light from the object travels to our eyes every bit nosotros sight along a line at the object. Similarly, nosotros see an epitome of an object because low-cal from the object reflects off a mirror and travel to our eyes equally we sight at the paradigm location of the object. From these 2 basic premises, we accept defined the image location as the location in space where light appears to diverge from. Ray diagrams have been a valuable tool for determining the path taken by light from the object to the mirror to our optics. In this section of Lesson 3, we will investigate the method for drawing ray diagrams for objects placed at various locations in front of a concave mirror.

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

• Whatsoever incident ray traveling parallel to the principal axis on the style to the mirror volition laissez passer through the focal point upon reflection.
• Whatsoever incident ray passing through the focal bespeak on the fashion to the mirror will travel parallel to the principal axis upon reflection.

Earlier in this lesson, the post-obit diagram was shown to illustrate the path of lite from an object to mirror to an centre.

In this diagram five incident rays are drawn along with their corresponding reflected rays. Each ray intersects at the image location and then diverges to the centre of an observer. Every observer would find the same image location and every light ray would follow the police of reflection. Yet only ii of these rays would be needed to determine the image location since it simply requires two rays to find the intersection bespeak. Of the five incident rays drawn, two of them correspond to the incident rays described past our two rules of reflection for concave mirrors. Because they are the easiest and near predictable pair of rays to depict, these will be the two rays used through the residue of this lesson.

Step-past-Step Method for Cartoon Ray Diagrams

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

1. Pick a point on the top of the object and depict 2 incident rays traveling towards the mirror.

Using a straight edge, accurately describe ane ray so that information technology passes exactly through the focal point on the way to the mirror. Describe the second ray such that it travels exactly parallel to the principal axis. Place arrowheads upon the rays to indicate their direction of travel.

2. In one case these incident rays strike the mirror, reflect them according to the two rules of reflection for concave mirrors.

The ray that passes through the focal point on the way to the mirror will reflect and travel parallel to the master centrality. Use a direct border to accurately draw its path. The ray that traveled parallel to the principal axis on the way to the mirror will reflect and travel through the focal point. Place arrowheads upon the rays to indicate their direction of travel. Extend the rays by their point of intersection.

3. Mark the prototype of the top of the object.

The paradigm betoken of the top of the object is the point where the two reflected rays intersect. If your were to draw a third pair of incident and reflected rays, then the tertiary reflected ray would likewise pass through this point. This is merely the indicate where all light from the top of the object would intersect upon reflecting off the mirror. Of class, the remainder of the object has an image as well and it tin can be found by applying the same three steps to some other called point. (See note below.)

4. Echo the process for the lesser of the object.

The goal of a ray diagram is to make up one's mind the location, size, orientation, and type of prototype that is formed by the concave mirror. Typically, this requires determining where the image of the upper and lower extreme of the object is located and then tracing the entire image. After completing the first iii steps, but the image location of the top extreme of the object has been found. Thus, the procedure must be repeated for the point on the bottom of the object. If the bottom of the object lies upon the chief centrality (as it does in this example), and then the image of this bespeak will also lie upon the main axis and be the same distance from the mirror as the image of the top of the object. At this point the entire epitome tin can exist filled in.

Some students take difficulty understanding how the entire image of an object tin can exist deduced once a unmarried point on the prototype has been determined. If the object is a vertically aligned object (such every bit the arrow object used in the example beneath), and so the process is like shooting fish in a barrel. The epitome is merely a vertical line. In theory, information technology would be necessary to option each point on the object and draw a dissever 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, then the prototype is also a vertical line. For our purposes, we volition but deal with the simpler situations in which the object is a vertical line that has its lesser located upon the master axis. For such simplified situations, the image is a vertical line with the lower extremity located upon the principal axis.

The ray diagram in a higher place illustrates that when the object is located at a position beyond the center of curvature, the epitome is located at a position betwixt the heart 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 we wish to obtain from a ray diagram. These characteristics of the image will exist discussed in more particular in the adjacent section of Lesson 3.

One time the method of drawing ray diagrams is practiced a couple of times, it becomes as natural as breathing. Each diagram yields specific data about the image. The two diagrams below evidence how to decide image location, size, orientation and blazon for situations in which the object is located at the center of curvature and when the object is located betwixt the center of curvature and the focal bespeak.

It should exist noted that the process of constructing a ray diagram is the same regardless of where the object is located. While the upshot of the ray diagram (image location, size, orientation, and blazon) is dissimilar, the same ii rays are ever drawn. The two rules of reflection are applied in order to determine the location where all reflected rays appear to diverge from (which for real images, is as well the location where the reflected rays intersect).

In the three cases described in a higher place - the case of the object existence located across C, the instance of the object being located at C, and the case of the object being located betwixt C and F - light rays are converging to a point afterward reflecting off the mirror. In such cases, a real epitome is formed. As discussed previously, a real image is formed whenever reflected light passes through the image location. While plane mirrors always 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 one 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 and so, a ray diagram tin can be used.

Watch Information technology!

A physics instructor discusses the nature of a existent image using a phun physics demonstration.

Ray Diagram for the Formation of a Virtual Image

A ray diagram for the case in which the object is located in front end of the focal signal is shown in the diagram at the right. Observe that in this example the low-cal rays diverge later on reflecting off the mirror. When light rays diverge after reflection, a virtual prototype is formed. As was done with plane mirrors, the prototype location can be 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 image point. Since light does not really pass through this betoken (calorie-free never travels behind the mirror), the image is referred to every bit a virtual paradigm. Observe that when the object in located in forepart of the focal point, its image is an upright and enlarged prototype that is located on the other side of the mirror. In fact, one generalization that tin be made about all virtual images produced past 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 Betoken

Thus far we have 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 end of F). But what happens when the object is located at F? That is, what type of epitome is formed when the object is located exactly one focal length from a concave mirror? Of course a ray diagram is e'er ane tool to help find 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 top extremity of the object and passes through the focal point does non run across the mirror. Thus, a different incident ray must exist used in society to determine the intersection point of all reflected rays. Any incident low-cal ray would work as long as it meets up with the mirror. Recall that the but reason that we have used the two we have is that they can be conveniently and hands drawn. The diagram beneath shows two incident rays and their corresponding reflected rays.

For the case of the object located at the focal bespeak (F), the lite 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. Afterward, the lite rays will non converge on the object's side of the mirror to form a real prototype; nor can they be extended backwards on the contrary side of the mirror to intersect to form a virtual image. And then 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 point, in that location is no location in space at which an observer can sight from which all the reflected rays appear to exist diverging. An image is non formed when the object is located at the focal bespeak of a concave mirror.

Nosotros Would Like to Suggest ...

Why just read virtually it and when you could be interacting with it? Collaborate - that's exactly what you do when you use one of The Physics Classroom's Interactives. Nosotros would like to propose that you combine the reading of this page with the use of our Optics Bench Interactive or our Name That Image Interactive. You can observe this in the Physics Interactives section of our website. The Optics Demote Interactive provides the learner an interactive enivronment for exploring the germination of images by lenses and mirrors. The Name That Paradigm Interactive provides learners with an intensive mental workout in recognizing the image characteristics for whatever given object location in front of a curved mirror.

Cheque Your Understanding

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

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Source: https://www.physicsclassroom.com/class/refln/Lesson-3/Ray-Diagrams-Concave-Mirrors

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