# Inconsistency in ray diagram

This example purports to show reflection of light rays from a spherical mirror. It looks good, until you try to draw a ray from the tip of the candle flame, then through the focal point, $$F$$, and then emerging parallel to the optic axis $$(CF)$$.

Go ahead, draw it on your computer monitor screen, or print this page and draw it on the paper. Whoops! This ray should then pass through the image of the tip of the candle flame, but it doesn't!

Here's what you get when you draw the third light ray (in red) from the candle flame. It comes nowhere near the image of the candle flame. As soon as you draw some of the "missing" rays, you discover that the diagram becomes inconsistent.

According to me, the diagram seems to be perfect. From where did this anomaly come from? Please help.

You have just shown the effect of spherical aberration.

Here is an accurate drawing showing that even when parallel to the principal axis rays after reflection do not meet at a point.

Here is an example which you may see when having a drink and a caustic is produced.

It is true. There is nothing wrong with the diagram. A large spherical mirror will not give you a perfect image.

• Will all the rays meet if they were paraxial? – SarGe May 10 at 14:05
• For a parabolic mirror, rays parallel to the axis will meet at the focus. A spherical mirror is an approximation if the size of the mirror is not too large compared to radius of curvature. – Charles Francis May 10 at 14:11

Interesting question ! Check out the link below which incorporates the ray you are questioning. Place the object roughly midway between C and F as in your diagram then play with the object height slider. You can see that as the object gets smaller the rays are more paraxial and they do meet at the same point after reflection from the mirror whereas as the object gets larger (and the situation is less paraxial) although they are still shown as meeting the ray through F would have to extend beyond the mirror surface to produce the required horizontal reflection.

The ray optics using spherical mirrors is just an approximation. In reality, a spherical mirror does not have a true focus. This is why the anomaly happens.

I think there is no anomaly. In the figure shown, the location of points C and F is not compatible with the curvature of mirror.

Correct either the location of these points or the curvature, and then check

• How so? The mirror may not be perfectly drawn, but C does appear to be at the center and f = c/2 as expected. Did you check out the link in my answer above? – Not_Einstein May 13 at 13:57