# Spherical aberration and concave mirrors

• jnimagine
In summary, the concave mirror experiment showed that when an object is placed at the focal point, an image does form but it is very far away from the focus. This has to do with spherical aberration and the thickness of the candle.
jnimagine
Concave mirror experiment

We did an experiment with a concave mirror
Concave mirror was placed on optics bench and a candle was placed at designated spots. A screen was used to see where the image was projected. But a strange thing happened. When the object was placed at the focal point, image was projected on the screen very far back of the bench. In theory, when the object is placed at the focus, no image is formed but in this experiment, image did form
Can anyone explain why this happened?

A spherical mirror cannot produce a perfect point image of a perfect point object. The usual simple spherical-mirror equation for image and object distance applies only as an approximation which gets better as the diameter of the mirror becomes smaller. This is called spherical aberration.

The Wikipedia article on spherical aberration illustrates this with a ray diagram for a lens with spherical surfaces, but the general principle is the same for a spherical mirror. Notice that the rays through the outer portions of the lens come together closer to the lens than the rays through the center of the lens. I think the same is true for mirrors, but my optics books are at the office and I'm at home now. (I better be at home in the middle of the night! )

How does spherical aberration cause an image to appear when the object is placed at the focus?

In theory, when the object is placed at the focus, no image should appear but when i did an experiment with a concave mirror and a candle, image did appear. But the image was very very far away from the focus but still on the image side.

Does this have anything to do with spherical aberration? or the thickness of the candle? because in theory, ur only talking about a single line and the candle posesses a thickness... maybe that has something to do with the image appearing?

Did you follow the link that I gave and look at the ray diagram there? In that diagram, the focal point is at the far right, but most of the rays actually converge to the left of the focal point because of spherical aberration. If we move the object (on the left side of the lens) from infinity to the focal point on that side, the rays that originally converged on the focal point on the right will now go out parallel (to an "image" at infinity), and the rays that originally converged closer to the lens will now converge to the left of infinity, at a large distance from the lens.

With spherical aberration, the image of a point object isn't a point any more, but instead a fuzzy spread-out blob in space. With the object at the focal point, some of that blob goes to infinity, but the rest doesn't.

jnimagine said:
Or the thickness of the candle? because in theory, ur only talking about a single line and the candle posesses a thickness... maybe that has something to do with the image appearing?

You nailed it.

While spherical (and other aberrations) may contribute to this effect, it is the defocus present (i.e. the fact that not all of your light source is in focus) that primarily ensures your image distance remains finite. You would still observe this effect in an aberration free lens.

Claude.

## 1. What is spherical aberration?

Spherical aberration is a type of optical aberration that occurs when a spherical lens or mirror is used to focus a beam of light. It causes the light rays to converge at different points, resulting in a blurred or distorted image.

## 2. How does spherical aberration affect concave mirrors?

Spherical aberration affects concave mirrors in a similar way as it affects spherical lenses. It causes the light rays to focus at different points, resulting in a distorted image. This can be a significant issue for concave mirrors used in optical systems, as it can lead to a loss of image clarity.

## 3. How can spherical aberration be corrected in concave mirrors?

Spherical aberration in concave mirrors can be corrected by using a parabolic shape instead of a spherical shape. This allows the light rays to converge at a single point, resulting in a sharper and clearer image. Additionally, using multiple smaller mirrors instead of one large mirror can also help reduce spherical aberration.

## 4. What factors can contribute to spherical aberration in concave mirrors?

Spherical aberration in concave mirrors can be caused by various factors, including the curvature and size of the mirror, the angle at which the light enters the mirror, and the wavelength of the light. The farther the light is from the center of the mirror, the greater the spherical aberration will be.

## 5. Can spherical aberration be completely eliminated in concave mirrors?

While it is possible to reduce spherical aberration in concave mirrors, it cannot be completely eliminated. This is due to the inherent nature of spherical surfaces and the way light behaves. However, by using corrective measures such as parabolic shapes and multiple mirrors, it is possible to minimize the effects of spherical aberration and achieve a high level of image quality.

• Optics
Replies
4
Views
1K
• Optics
Replies
172
Views
15K
• Optics
Replies
17
Views
2K
• Optics
Replies
2
Views
6K
• Optics
Replies
6
Views
3K
• Optics
Replies
6
Views
984
• Optics
Replies
9
Views
2K
• Optics
Replies
3
Views
2K
• Optics
Replies
3
Views
2K
• Optics
Replies
1
Views
2K