Concave mirror: Reflected rays do not meet at one point

In summary, an elliptical mirror will have some focusing going on, while a regular curved mirror will produce spherical aberration and coma.
  • #1
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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  • #2
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:
 
  • #3
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.
?
 
  • #4
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:
 
  • #5
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.
 
  • #6
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?
 
  • #7
Yes.
 
  • #8
jtbell said:
Yes.

Thanks now I know what to look for next.
 
  • #9
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.
 

1. What is a concave mirror?

A concave mirror is a curved mirror with a reflective surface that curves inward, like the inside of a bowl. It is also known as a converging mirror because it causes parallel rays of light to converge at a focal point.

2. Why do reflected rays not meet at one point in a concave mirror?

This is because the shape of a concave mirror causes the reflected rays to be diverging instead of converging. As the rays hit the curved surface, they are reflected at different angles, causing them to spread apart instead of coming together at a single point.

3. What is the focal point of a concave mirror?

The focal point is the point at which parallel rays of light will converge after reflecting off a concave mirror. It is located halfway between the center of curvature and the surface of the mirror.

4. How does the focal length affect the behavior of reflected rays in a concave mirror?

The focal length is the distance between the focal point and the center of curvature of a concave mirror. It determines how much the reflected rays will converge or diverge. A shorter focal length will result in a more pronounced convergence, while a longer focal length will cause the reflected rays to diverge less.

5. What are some common uses of concave mirrors?

Concave mirrors have a variety of applications, including in telescopes, microscopes, and headlights. They are also used in reflecting telescopes, solar cookers, and makeup mirrors. In addition, they are used in curved mirrors in amusement park attractions and security cameras to create a larger field of view.

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