How To Draw Ray Diagrams For Mirrors

Ray Diagrams - Concave Mirrors

The theme of this unit has been that we come across an object because light from the object travels to our eyes every bit we sight along a line at the object. Similarly, nosotros see an image of an object because light from the object reflects off a mirror and travel to our eyes equally nosotros sight at the image location of the object. From these ii basic premises, nosotros have defined the image location equally the location in infinite 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 iii, 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, nosotros volition have to call up the two rules of reflection for concave mirrors:

Any incident ray traveling parallel to the primary centrality on the mode to the mirror will pass through the focal point upon reflection.
Whatsoever incident ray passing through the focal signal on the way to the mirror will travel parallel to the principal 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 v incident rays are drawn along with their corresponding reflected rays. Each ray intersects at the paradigm location and then diverges to the eye of an observer. Every observer would observe the same image location and every lite ray would follow the law of reflection. Yet merely 2 of these rays would be needed to determine the image location since information technology but requires ii rays to find the intersection point. Of the 5 incident rays drawn, 2 of them correspond to the incident rays described past our two rules of reflection for concave mirrors. Considering they are the easiest and most predictable pair of rays to describe, these will be the 2 rays used through the remainder of this lesson.

Footstep-by-Footstep Method for Cartoon 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 centre of curvature (C) of a concave mirror. Yet the aforementioned method works for cartoon a ray diagram for whatever object location.

1. Pick a betoken on the top of the object and draw two incident rays traveling towards the mirror.

Using a straight edge, accurately draw one ray then that information technology passes exactly through the focal point on the way to the mirror. Depict the 2d ray such that it travels exactly parallel to the principal centrality. Place arrowheads upon the rays to indicate their direction of travel.

2. Once 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 mode to the mirror will reflect and travel parallel to the principal axis. Apply a straight edge to accurately draw its path. The ray that traveled parallel to the principal axis on the way to the mirror volition reflect and travel through the focal betoken. Identify arrowheads upon the rays to bespeak their direction of travel. Extend the rays past their point of intersection.

3. Mark the image of the top of the object.

The epitome point of the top of the object is the signal where the two reflected rays intersect. If your were to draw a tertiary pair of incident and reflected rays, and then the third reflected ray would also pass through this signal. This is merely the bespeak where all lite from the peak of the object would intersect upon reflecting off the mirror. Of course, the rest of the object has an image as well and it tin can exist found by applying the aforementioned three steps to another chosen betoken. (Meet note below.)

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

The goal of a ray diagram is to determine the location, size, orientation, and type of prototype that is formed by the concave mirror. Typically, this requires determining where the epitome of the upper and lower extreme of the object is located and then tracing the entire image. After completing the showtime three steps, only the paradigm location of the top extreme of the object has been establish. Thus, the process must be repeated for the point on the bottom of the object. If the bottom of the object lies upon the principal axis (as information technology does in this example), and then the paradigm of this point volition also lie upon the chief axis and be the same distance from the mirror as the image of the top of the object. At this signal the entire image can be filled in.

Some students have difficulty understanding how the entire image of an object tin can exist deduced one time a unmarried point on the epitome has been adamant. If the object is a vertically aligned object (such as the pointer object used in the case below), and then the process is easy. The epitome is merely a vertical line. In theory, it would exist necessary to pick each point on the object and depict a split ray diagram to determine the location of the prototype of that point. That would require a lot of ray diagrams every bit illustrated beneath.

Fortunately, a shortcut exists. If the object is a vertical line, so the image is also a vertical line. For our purposes, we will simply deal with the simpler situations in which the object is a vertical line that has its bottom located upon the principal axis. For such simplified situations, the image is a vertical line with the lower extremity located upon the principal axis.

The ray diagram to a higher place illustrates that when the object is located at a position across the center of curvature, the epitome is located at a position between the heart of curvature and the focal point. Furthermore, the prototype 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 detail in the next section of Lesson three.

Once the method of drawing ray diagrams is practiced a couple of times, information technology becomes as natural as breathing. Each diagram yields specific information virtually the image. The 2 diagrams below show how to determine image location, size, orientation and type for situations in which the object is located at the center of curvature and when the object is located between the heart of curvature and the focal point.

Information technology should exist noted that the process of amalgam a ray diagram is the same regardless of where the object is located. While the issue of the ray diagram (paradigm location, size, orientation, and type) is unlike, the same ii rays are always drawn. The two rules of reflection are applied in social club to determine the location where all reflected rays appear to diverge from (which for existent images, is besides the location where the reflected rays intersect).

In the iii cases described above - the case of the object being located across C, the instance of the object being located at C, and the case of the object being located betwixt C and F - calorie-free rays are converging to a point after reflecting off the mirror. In such cases, a real image is formed. As discussed previously, a real image is formed whenever reflected low-cal 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 altitude 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 then, a ray diagram can be used.

Lookout It!

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

Ray Diagram for the Germination of a Virtual Prototype

A ray diagram for the case in which the object is located in front of the focal point is shown in the diagram at the right. Observe that in this instance the light rays diverge after reflecting off the mirror. When low-cal rays diverge after reflection, a virtual image is formed. Equally was done with plane mirrors, the paradigm location tin can be constitute 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 indicate of intersection of the extended reflected rays is the prototype point. Since calorie-free does non actually pass through this signal (light never travels backside the mirror), the image is referred to as a virtual image. Observe that when the object in located in forepart of the focal point, its prototype is an upright and enlarged image that is located on the other side of the mirror. In fact, one generalization that tin be fabricated about all virtual images produced by mirrors (both plane and curved) is that they are always upright and e'er located on the other side of the mirror.

Ray Diagram for an Object Located at the Focal Point

Thus far we have seen via ray diagrams that a real paradigm is produced when an object is located more than one focal length from a concave mirror; and a virtual paradigm is formed when an object is located less than one focal length from a concave mirror (i.e., in front end of F). Simply what happens when the object is located at F? That is, what blazon of image is formed when the object is located exactly ane focal length from a concave mirror? Of class a ray diagram is ever one tool to help find the answer to such a question. Yet, when a ray diagram is used for this instance, an immediate difficulty is encountered. The incident ray that begins from the tiptop extremity of the object and passes through the focal signal does not meet the mirror. Thus, a dissimilar incident ray must be used in order to determine the intersection point of all reflected rays. Any incident lite ray would work equally long as it meets upwardly with the mirror. Recall that the only reason that nosotros have used the two nosotros accept is that they tin can be conveniently and easily fatigued. The diagram below shows two incident rays and their respective reflected rays.

For the instance of the object located at the focal point (F), the light rays neither converge nor diverge later on reflecting off the mirror. As shown in the diagram above, the reflected rays are traveling parallel to each other. Subsequently, the light rays will non converge on the object's side of the mirror to form a real paradigm; nor can they exist extended backwards on the opposite side of the mirror to intersect to course a virtual image. 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 indicate, there is no location in space at which an observer tin can sight from which all the reflected rays appear to be diverging. An prototype is not formed when the object is located at the focal point of a concave mirror.

We Would Similar to Suggest ...

Why just read nigh it and when you could be interacting with information technology? Interact - that'due south exactly what yous do when you lot apply one of The Physics Classroom'due south Interactives. We would similar to suggest that you combine the reading of this page with the use of our Optics Bench Interactive or our Name That Image Interactive. Yous can find this in the Physics Interactives department of our website. The Optics Demote Interactive provides the learner an interactive enivronment for exploring the formation of images by lenses and mirrors. The Name That Paradigm Interactive provides learners with an intensive mental workout in recognizing the prototype characteristics for any given object location in front of a curved mirror.

Check Your Understanding

The diagram below shows two light rays emanating from the summit 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 law of reflection.