2. Key rays used in ray tracing. Figure 3-17 shows three key rays—for each mirror—that are used to locate an image point corresponding to a given object point. They are

labeled 1, 2, and 3. Any two, drawn from object point P, will locate the corresponding image point P′. In most cases it is sufficient to locate one point, like P′, to be able to draw the entire image. Note carefully, with reference to Figure 3-17a, b, the following facts:

For a concave mirror:

• The ray from object point P parallel to the axis, such as ray 1, reflects from the mirror and passes through the focal point F (labeled ray 1').
• The ray from P passing through the focal point F, such as ray 2, reflects from the mirror as a ray parallel to the axis (labeled ray 2').
• The ray from P passing through the center of curvature C, such as ray 3, reflects back along itself (labeled ray 3').
• Reflected rays 1', 2', and 3' converge to locate point P′ on the image. This image is a real image that can be formed on a screen located there.

For a convex mirror:
• The ray from object point P, parallel to the axis, such as ray 1, reflects from the mirror as if to come from the focal point F behind the mirror (labeled ray 1').
• The ray from P, such as ray 2, headed toward the focal point F behind the mirror, reflects from the mirror in a direction parallel to the optical axis (labeled ray 2').
• The ray from P, such as ray 3, headed toward the center of curvature C behind the mirror, reflects back along itself (labeled ray 3').
• Rays 1', 2', and 3' diverge after reflection. A person looking toward the mirror intercepts the diverging rays and sees them appearing to come from their common intersection point P′, behind the mirror. The image is virtual since it cannot be formed on a screen placed there.

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