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Question
How to draw ray diagrams of the convex mirrors?
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Solution
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; this ray will strike the mirror before reaching the focal point; 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.
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 you 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. Of course, the rest of the object has an image as well and it can be found by applying the same three steps for another chosen point.
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. 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 complete image can be filled in.
Using a straight edge, accurately draw one ray so that it travels towards the focal point on the opposite side of the mirror; this ray will strike the mirror before reaching the focal point; 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.
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 you 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. Of course, the rest of the object has an image as well and it can be found by applying the same three steps for another chosen point.
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. 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 complete image can be filled in.
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