Yes, spherical aberration has something to do with it. I went away and wrote something about this, and did a calculation to show how spherical aberration can contribute to this effect. I will post it as I wrote it without trying to connect it to andrevdh's reply. I hope the connection will be obvious when you read them both.
I fully expect that the image you saw was blurry, but the variation in the focal length of a spherical mirror for off-axis rays could explain why an image forms at all. I dare say you would have had a very difficult time deciding where the image that you observed was located. If you were seeing a sharp image, your candle was not at the focal point.
If you look carefully at the pictures of the light beams at the link I posted
http://www.physics.montana.edu/demonstrations/video/6_optics/demos/sphericalaberrationinamirror.html
you will observe another interesting effect. The focal point for one of the individual narrow off-axis beams is itself off axis. If you blocked off the inner part of the mirror, so that only the outer beams were visible, and if the surface were rotated about the axis to make a three dimensional image, the sharpest image would be a ring around the axis. It would not even be a point on the axis.
This is a complicated effect to analyze in detail. Your candle could not possibly have been
at the focal point even if there was a precise focal point. The candle is a three dimensional object. The focal point is a point (ideally; not actually). Some of the candle was no doubt in front (closer to mirror) of the focal point and some of it was behind the focal point. An image of such an object would actually be three dimensional, even if the focal point were ideal. There is no way you can get a very precise image of a three dimensional object on a screen. What you were seeing could be in part due to the part of the candle that was outside the focal point coming to focus far from the mirror.
It is a rather complicated calculation to figure out where light that leaves the nominal focal point of a spherical mirror comes to focus on the mirror axis. I have done that calculation, and I could post the equations that shows the location of the “image” in terms of the angle between the mirror axis and a radius to a point on the mirror. For small angles, the distance from the mirror is enormous, approaching infinity as the angle approaches zero. But as the angle increases, the image gets closer and closer to the center of the circle. If you went out as far as 60 degrees, the image would be only one radius from the center of the sphere. Of course your mirror does not go to 60 degrees.
If you stop there, you would conclude that the image is just smeared along the entire length of the axis, and that is sort of true. But there is more to it than that. The fact is that each ring of say one-degree width at larger distances from the axis has greater area, and that means that more light energy is reflected from off-axis rings. Not only that, the light from an off-axis ring of is more tightly focused along the length of the axis than the weaker light from a ring closer to the axis. The figure I am posting here is a good approximation to the light energy per unit length along the axis from rings of one-degree width from zero to 15 degrees. At 15 degrees the “image” is only about 15 radii, or 30 focal lengths from the mirror, The light from the inner rings is so much less intense and so smeared out that it has almost no effect on image formation. There is much more energy from the last few degrees of the mirror, and that energy is relatively well focused.
There is enough focusing from the aberration effect to create a blurry image of the candle far from the mirror. The three dimensional nature of the candle flame would also make a contribution. I would be interested to know how many focal lengths it was from the mirror to the image you were seeing, and how well you think you could measure that distance. My guess is it was pretty far away, and not very well defined.
it's not supposed to be 0.5f...
