|
Select Tab to Verify
Course Approval Status:
ABO # STWQO034-2
APPROVED for 1 Hour(s) of CE
New York - (#09-01) DISP
APPROVED for 1 Hour(s) of CE
Florida
NOT APPROVED for 1 Hour(s) of CE
Tennessee Approval Pending
PENDING for 1 Hour(s) of CE
Nevada - SP
APPROVED for 1 Hour(s) of CE
Ohio - SP
APPROVED for 1 Hour(s) of CE
Georgia
PENDING for 1 Hour(s) of CE
Ontario Opticians (#2674 EG)
APPROVED for 1 Hour(s) of CE |
| Author Information |
 |
| E-Mail Author |
17
41
In this diagram there are two rays traveling parallel to the axis, a red ray and a white ray. Both reflect from the surface through the center of curvature. Looking just at the white ray, the angle of incidence and the angle of reflection are equal, so they are both equal to the angle of incidence (< I). The incident white ray and the axis are parallel to each other. The normal to the white ray crosses both the white ray and the axis. A rule in geometry is that the opposite interior angles formed by three lines are equal, when two of the lines are parallel. So the angle between the dotted white line and the axis equals < i. Now look at the triangle formed by the reflected ray, the normal, and the axis. It has two angles that are both equal to < i, and therefore that triangle is an isosceles triangle. That means that two sides are equal, and therefore the distance from the point of reflection to the focal point is equal to the distance from the focal point to the center of curvature. Look at the red ray and it's reflection. The same triangle forms here, but it is harder to see because it is so close to the axis. The closer the ray is to the axis, the closer the distance reflection side of the triangle will be to the distance from the mirror to the focal point on the axis. Because the white ray is not ‘close’ to the axis the reflection of this ray shows spherical aberration. The white ray is a peripheral ray, and spherical aberration is a peripheral aberration. The red ray, because it is paraxial, or close to the axis, shows much less aberration. Therefore, the focal point of a concave mirror is at 1/2 the distance from the center of curvature to the mirror. If the radius of the mirror, which is the distance from the center of curvature to the mirror, is 10 cm, then the focal length of the mirror will be 1/2 of 10 cm), or 5 cm. In this case, what is the power of the mirror? The power of the mirror is found the same way that the power of a lens is found: by dividing 1 by the focal length in meters. 5 cm = 0.05 meters, and the power is 1/0.05 = 20 Diopters. The rule for a ray traveling parallel to the axis is that it will reflect through the focal point. And since the path of a ray is reversible, the ray that travels through the focal point will reflect parallel to the axis. |
|
