Question on Focal Point. What is the focal point in the diagram link where object and image is at same point?

Question

http://server2.uploadit.org/files/jazzy123-lensqn.JPG

Answer 1

The way to answer this, is to first assume that the focal point is somewhere between the object and lens.  Try drawing a ray through the focal point.  As you should have learned, a ray from tip of object, through focal point, will be horizontal when it goes to other side of lens.

Then, the mirror reflects it back into lens -- still horizontal!  So the ray ends up going right back through the object.   Then, if you draw the ray from tip of object, through center of lens, (which is undeviated), then reflect off the mirror, you will find that these two rays do not intersect on the object side-- so the object and image are NOT in the same place.

You get the same answer if the focal point is to the right of the object.  So ... focal point can't be between object and lens, and it can't be right of object ... next thing to try is right AT the object!

In this case, since the object is at the focal point, all rays from the object end up parallel on the other side of the lens.  Then, the mirror reflects them, but they are still parallel going back through the lens -- which means that they will image to a point on the focal plane.  So, that is the only answer that works!