Concave mirror: Reflected rays do not meet at one point

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Discussion Overview

The discussion revolves around the behavior of reflected rays from a concave mirror, particularly focusing on why they may not converge at a single point. Participants explore concepts related to spherical and elliptical mirrors, aberrations, and the implications of ray geometry.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant presents a diagram showing incident and reflected rays from a concave mirror, questioning why they do not meet at one point.
  • Another participant notes that only special geometries, such as elliptical mirrors, guarantee convergence of rays from a point source, while regular curved mirrors may focus rays but not necessarily at a single point.
  • Several participants discuss the concept of spherical aberration, indicating that a spherical mirror produces a point image only under certain conditions, specifically in the paraxial approximation.
  • There is mention of coma as another aberration affecting the convergence of rays, particularly when the object is off-axis.
  • Participants inquire about the implications of placing an object on the optical axis and how it affects ray convergence.
  • Some participants express a need for additional resources to better understand the phenomena discussed, indicating dissatisfaction with their current textbook.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the specifics of ray convergence in concave mirrors, with multiple competing views on the effects of spherical aberration and coma, as well as the conditions under which rays converge.

Contextual Notes

Limitations include the dependence on specific geometrical configurations and the unresolved nature of how different types of aberrations affect ray behavior in practical scenarios.

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I have drawn a diagram of the incident and reflected rays of an object by the concave mirror. Red color shows the incident rays, black color shows the normals drawn from the center of curvature, while green color shows the reflected rays. Shouldn't all the reflected rays meet at one point.

Any suggestions are welcome.

26b0a48.jpg
 
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It's only for special geometries that rays coming off of a curved mirror will converge on a single point, if they diverged from a point source.
In particular, an elliptical cavity has this special property that light rays diverging from one ficus will converge on the second focus.

Ellipse or no, there will be some focusing going on with a regular curved mirror. This is why, for example, it is highly inadvisable to have glass buildings with curved surfaces:

See for example:
 
Does this mean that...
1. My diagram is correct.
2. The rays will truly converge in the case of ellipse concave mirrors only.
3. In case of spherical mirrors, not all the rays will converge, but maximum will converge at one point. Parallel rays, rays passing though curvature, rays passing through focus point or rays directed to pole will converge exactly at one point.
?
 
Does this mean that...
1. My diagram is correct.
2. The rays will truly converge in the case of ellipse concave mirrors only.
3. In case of spherical mirrors, not all the rays will converge, but maximum will converge at one point. Parallel rays, rays passing though curvature, rays passing through focus point or rays directed to pole will converge exactly at one point.
?
jfizzix said:
It's only for special geometries that rays coming off of a curved mirror will converge on a single point, if they diverged from a point source.
In particular, an elliptical cavity has this special property that light rays diverging from one ficus will converge on the second focus.

Ellipse or no, there will be some focusing going on with a regular curved mirror. This is why, for example, it is highly inadvisable to have glass buildings with curved surfaces:

See for example:
 
Look up spherical aberration. A spherical mirror produces a point image of a point object only in the paraxial approximation, in which the rays don't make large angles to the optical axis, and we use only a small part of the spherical surface, close to the point where the optical axis intersects it.
 
jtbell said:
Look up spherical aberration. A spherical mirror produces a point image of a point object only in the paraxial approximation, in which the rays don't make large angles to the optical axis, and we use only a small part of the spherical surface, close to the point where the optical axis intersects it.
Is my diagram, actually showing "spherical aberration" in effect?
 
Yes.
 
jtbell said:
Yes.

Thanks now I know what to look for next.
 
Your diagram is illustrating coma, an aberration of an off-axis object.

If you put your object on the axis, you should get better convergence of the reflected rays.
 
  • #10
Right, it has both spherical aberration and coma. If the object and image are on-axis, you still get spherical aberration. Unless the object is at the center of curvature, in which case the image is also at the center of curvature... not a very useful situation!
 
  • #11
pixel said:
Your diagram is illustrating coma, an aberration of an off-axis object.

If you put your object on the axis, you should get better convergence of the reflected rays.
What is meant by putting an object on the axis? Does it mean that the principal axis bisect an object?
 
  • #12
We (pixel and I) are talking about point-objects. In your diagram, the tail of the arrow is on the optical axis of the mirror. All other points on the arrow, including the tip from which you drew your rays, are off axis.
 
  • #13
jtbell said:
We (pixel and I) are talking about point-objects. In your diagram, the tail of the arrow is on the optical axis of the mirror. All other points on the arrow, including the tip from which you drew your rays, are off axis.
Any good books or sites that can help me understand these phenomenons in a step by step manner? I think my textbook is not well planned.
 

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