Why Did an Image Form at the Focal Point in Our Concave Mirror Experiment?

[jnimagine]

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?

 

[OlderDan]

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 concave mirror that has a precise focal point would be in the shape of a paraboloid. The mirror you used was almost surely a spherical mirror. The focal length of such a mirror is nominally half the radius of curvature of the mirror. That works very well for rays that are nearly parallel to and close to the axis. As you move off axis, the focal point changes.

Draw a right side semicircle to represent a mirror, and locate a point half way between the center and the arc. This is the focal point for near-axis rays. Draw a radius from the center of the circle to the arc at 45 degrees to the horizontal. Draw a horizontal ray that meets this radius on the arc. This ray will be reflected 90 degrees to be vertical. Where does this ray intersect the axis of the mirror in comparison to the nominal focal point? Now draw a ray from the focal point to meet the raduis on the arc. Where will this ray be reflected? Can you begin to see how an image might form?

You might want ot look up spherical aberration on the internet. For example

http://www.physics.montana.edu/demonstrations/video/6_optics/demos/sphericalaberrationinamirror.html

 

[andrevdh]

If I understood your description correctly it suggest that a spherically concave mirror should form a virtual image on the other side of the mirror if the object is located at its focal point?

 

[OlderDan]

If I understood your description correctly it suggest that a spherically concave mirror should form a virtual image on the other side of the mirror if the object is located at its focal point?

The image was formed on a screen, so it had to be a real image, and it would have to be on the same side of the mirror as the object. I interpret "back of the bench" to mean far from the mirror, but on the image side.

 

[jnimagine]

A concave mirror that has a precise focal point would be in the shape of a paraboloid. The mirror you used was almost surely a spherical mirror. The focal length of such a mirror is nominally half the radius of curvature of the mirror. That works very well for rays that are nearly parallel to and close to the axis. As you move off axis, the focal point changes.

Draw a right side semicircle to represent a mirror, and locate a point half way between the center and the arc. This is the focal point for near-axis rays. Draw a radius from the center of the circle to the arc at 45 degrees to the horizontal. Draw a horizontal ray that meets this radius on the arc. This ray will be reflected 90 degrees to be vertical. Where does this ray intersect the axis of the mirror in comparison to the nominal focal point? Now draw a ray from the focal point to meet the raduis on the arc. Where will this ray be reflected? Can you begin to see how an image might form?

You might want ot look up spherical aberration on the internet. For example

http://www.physics.montana.edu/demonstrations/video/6_optics/demos/sphericalaberrationinamirror.html

I still don't really get why the image would form. Isn't spherical aberration just mean the bluriness of the image? How does the rays not meeting at one point have an effect on showing the image? Spherical aberration might cause the images to be blurry but not make an image appear when it's not supposed to be...

 

[andrevdh]

My take on the situation is that the image switches from positive infinity (real image) to minus infinity (virtual image) as one moves the object through the focal point. To locate it accurately experimentally is not an easy task. So my guess is that the object was not yet at the focal plane of the mirror and had to be moved a little further.

 

[OlderDan]

I still don't really get why the image would form. Isn't spherical aberration just mean the bluriness of the image? How does the rays not meeting at one point have an effect on showing the image? Spherical aberration might cause the images to be blurry but not make an image appear when it's not supposed to be...

I see that you started another thread related to this topic, and I know that andrevdh is also trying to help you with this. I will post something on the other thread that is related to what andrevdh posted.