Ray Diagrams
The line of sight principle suggests
that in order to view an image of an object in a mirror, a person must sight
along a line at the image of the object. When sighting along such a line, light
from the object reflects off the mirror according to the law of
reflection and travels to the person's eye. This process was discussed and
explained earlier in this lesson. One useful tool that is
frequently used to depict this idea is known as a ray diagram. A ray diagram is a
diagram that traces the path that light takes in order for a person to view a
point on the image of an object. On the diagram, rays (lines with arrows) are
drawn for the incident ray and the reflected ray. Complex objects such as
people are often represented by stick figures or arrows. In such cases it is
customary to draw rays for the extreme positions of such objects.
Drawing Ray
Diagrams - a Step-by-Step Approach
This section of Lesson 2 details and illustrates the
procedure for drawing ray diagrams. Let's begin with the task of drawing a ray
diagram to show how Suzie will be able to see the image of the green object
arrow in the diagram below. For simplicity sake, we will suppose that Suzie is
viewing the image with her left eye closed. Thus, we will focus on how light
travels from the two extremities of the object arrow (the left and right side)
to the mirror and finally to Suzie's right eye as she sights at the image. The
four steps of the process for drawing a ray diagram are listed, described and
illustrated below.
1. Draw the image of the object.
Use the
principle that the object distance is equal to the image distance to determine
the exact location of the object. Pick one extreme on the object and carefully measure
the distance from this extreme
point to the mirror. Mark off
the same distance on the opposite side of the mirror and mark the image of this extreme point. Repeat this
process for all extremes on the object until you have determined the complete
location and shape of the image. Note that all distance measurements should be
made by measuring along a segment that is perpendicular to the mirror.
2. Pick one extreme on the image of the object and draw the
reflected ray that will travel to the eye as it sights at this point.
Use the line of sight principle: the eye
must sight along a line at the image of the object in order to see the image of
the object. It is customary to draw a bold line for the reflected ray (from the
mirror to the eye) and a dashed line as an extension of this reflected ray; the
dashed line extends behind the mirror to the location of the image point. The
reflected ray should have an arrowhead upon it to indicate the direction that
the light is traveling. The arrowhead should be pointing towards the eye since
the light is traveling from the mirror to the eye, thus enabling the eye to see
the image.
3. Draw the incident ray for light traveling from the
corresponding extreme on the object to the mirror.
The
incident ray reflects at the mirror's surface according to the law of reflection. But rather than measuring
angles, you can merely draw the incident ray from the extreme of the object to the point of
incidence on the mirror's surface. Since you drew the reflected ray in step 2,
the point of incidence has already been determined; the point of incidence is
merely the point where the line of sight intersects the mirror's surface. Thus
draw the incident ray from the extreme
point to the point of
incidence. Once more, be sure to draw an arrowhead upon the ray to indicate its
direction of travel. The arrowhead should be pointing towards the mirror since
light travels from the object to the mirror.
4. Repeat steps 2 and 3 for all other extremities on the
object.
After
completing steps 2 and 3, you have only shown how light travels from a single extreme on the object to the mirror and
finally to the eye. You will also have to show how light travels from the other extremes on the object to the eye. This is
merely a matter of repeating steps 2 and 3 for each individual extreme. Once
repeated for each extreme, your ray diagram is complete.
Your Turn to Practice
The best way to learn to draw ray diagrams involves trying it
yourself. It's easy. Merely duplicate the two setups below onto a blank sheet
of paper, grab a ruler/straightedge, and begin. If necessary, refer to the
four-step procedure listed above. When finished, compare your diagram with the
completed diagrams at the bottom of this page.
Uses
of Ray Diagrams
Ray diagrams can be particularly useful for determining and explaining
why only a portion of the image of an object can be seen from a given location.
The ray diagram at the right shows the lines of sight used by the eye in order
to see a portion of the image in the mirror. Since the mirror is not long
enough, the eye can only view the topmost portion of the image. The lowest
point on the image that the eye can see is that point in line with the line of
sight that intersects the very bottom of the mirror. As the eye tries to view
even lower points on the image, there is not sufficient mirror present to
reflect light from the lower points on the object to the eye. The portion of
the object that cannot be seen in the mirror is shaded green in the diagram
below.
Similarly, ray diagrams are useful tools for determining and
explaining what objects might be viewed when sighting into a mirror from a
given location. For example, suppose that six students - Al, Bo, Cy, Di, Ed, and Fred sit in front
of a plane mirror and attempt to see each other in the mirror. And suppose
the exercise involves answering the following questions: Whom can Al see? Whom
can Bo see? Whom can Cy see? Whom can Di
see? Whom can Ed see? And whom can Fred see?
The task begins by locating the images of the given students.
Then, Al is isolated from the rest of the students and lines of sight are drawn
to see who Al can see. The leftward-most student whom Al can see is the student
whose image is to the right of the line of sight that intersects the left edge
of the mirror. This would be Ed. The rightward-most student who Al can see is
the student whose image is to the left of the line of sight that intersects the
right edge of the mirror. This would be Fred. Al could see any student
positioned between Ed and Fred by looking at any other positions along the
mirror. However in this case, there are no other students between Ed and Fred;
thus, Ed and Fred are the only students whom Al can see? The diagram below
illustrates this using lines of sight for Al.
Of course the same process can be repeated for the other students by
observing their lines of sight. Perhaps you will want to try to determine whom
Bo, Cy, Di, Ed, and Fred can see? Then check your
answers by clicking the button below.
Bo can see Di, Ed, and Fred
Cy can see Cy, Di, Ed,
and Fred
Di can see Cy, Di, Ed, and Fred
Ed can see Bo, Cy, Di, and Eve
Fred can see Al,
Bo, Cy, and Di
Check Your Understanding
1. Six students are arranged in front of a mirror. Their
positions are shown below. The image of each student is also drawn on the
diagram. Make the appropriate line of sight constructions to determine that
students each individual student can see.
Al can see Ed and Fred
Bo can see Ed, and Fred
Cy can see Cy, Di, Ed,
and Fred
Di can see Cy, Di, and Ed,
Ed can see Al, Bo, Cy, Di, and Ed
Fred can see
Bo, Cy, Di, and Ed
Here are completed diagrams for the two examples given above
in the Your Turn to Practice section.
Back to Diagram.