Spherical aberration and concave mirrors

[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?

 

[jtbell]

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! )

 

[jnimagine]

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?

 

[jtbell]

[By the way, please don't start a new thread when you're continuing the same topic. I merged your two threads together.]

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.

 

[Claude Bile]

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.