Question

Write the four rules for construction of image by ray diagram (for convex mirror and concave mirror).

Answer 1

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

Any incident ray traveling parallel to the principal axis on the way to the mirror will pass through the focal point upon reflection.Any incident ray passing through the focal point on the way to the mirror will travel parallel to the principal axis 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 image location and then diverges to the eye of an observer. Every observer would observe the same image location and every light ray would follow the law of reflection. Yet only two of these rays would be needed to determine the image location since it only requires two rays to find the intersection point. Of the five incident rays drawn, two 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 draw, these will be the two rays used through the remainder of this lesson.

 

Step-by-Step Method for Drawing Ray Diagrams

The method for drawing 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 center of curvature (C) of a concave mirror. Yet the same method works for drawing a ray diagram for any object location.

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

Using a straight edge, accurately draw one ray so that it passes exactly through the focal point on the way to the mirror. Draw 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. 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 way to the mirror will reflect and travel parallel to the principal axis. Use a straight edge 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 past their point of intersection.

 

3. Mark the image 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 third pair of incident and reflected rays, then the third reflected ray would also pass through this point. This is merely the point where all light from the top of the object would intersect upon reflecting off the mirror. Of course, the rest of the object has an image as well and it can be found by applying the same three steps to another chosen point. (See note below.)

 

 

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

The goal of a ray diagram is to determine the location, size, orientation, and type of image 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 three steps, only the image location of the top extreme of the object has been found. 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 it does in this example), then the image of this point will also lie upon the principal axis and be the same distance from the mirror as the image of the top of the object. At this point the entire image can be filled in.

 

 

Some students have difficulty understanding how the entire image of an object can be deduced once a single point on the image has been determined. If the object is a vertically aligned object (such as the arrow object used in the example below), then the process is easy. The image is merely a vertical line. In theory, it would be necessary to pick each point on the object and draw a separate ray diagram to determine the location of the image 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 image is also 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 principal axis. For such simplified situations, the image is a vertical line with the lower extremity located upon the principal axis.

Answer 2

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

Explanation:

The steps for ray diagram are given below :

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

• Using a straight edge, accurately draw one ray so that it travels towards the focal point on the opposite side of the mirror
• stop the ray at the point of incidence with the mirror.
• Draw 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. Once these incident rays strike the mirror, reflect them according to the two rules of reflection for convex mirrors.

• The ray that travels towards the focal point will reflect and travel parallel to the principal axis.
• Use a straight edge to accurately draw its path.

• The ray that traveled parallel to the principal axis on the way to the mirror will reflect and travel in a direction such that its extension passes through the focal point.
• Align a straight edge with the point of incidence and the focal point, and draw the second reflected ray.
• Place arrowheads upon the rays to indicate their direction of travel.
• The two rays should be diverging upon reflection.  

3. Locate and mark the image of the top of the object.

• The image point of the top of the object is the point where the two reflected rays intersect.
• Since the two reflected rays are diverging, they must be extended behind the mirror in order to intersect.
• Using a straight edge, extend each of the rays using dashed lines. Draw the extensions until they intersect.
• The point of intersection is the image point of the top of the object. Both reflected rays would appear to diverge from this point.
• If your were to draw a third pair of incident and reflected rays, then the extensions of the third reflected ray would also pass through this point. This is merely the point where all light from the top of the object would appear to diverge from upon reflecting off the mirror.

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

• The goal of a ray diagram is to determine the location, size, orientation, and type of image that is formed by the convex mirror.
• After completing the first three steps, only the image location of the top extreme of the object has been found. 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 then the image of this point will also lie upon the principal axis and be the same distance from the mirror as the image of the top of the object.

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