Angular Magnification for mirrors and lens

[jix]

Homework Statement

I'm looking for someone to clarify a strange result regarding angular magnification. For both mirrors and lens.

Homework Equations

m(angular) = θ'/θ
M(lateral) = h'/h = - d'/d
θ ≈ h/d (for small angles)

The Attempt at a Solution

Using the angle equation, I get a result that looks like:

m(angular) = (h'/h) * (d/d')

But since h'/h = -d'/d, I get m(angular) = -1, regardless of the angles, distances, etc. Is this wrong, or is it true that for small angles the magnification is actually always -1?

Thanks to everyone in advance.

 

[turin]

Angular magnification is typically relevant for situations where the lateral magnification is formally infinite. For instance, a microscope's job is to make tiny objects "look big", but just as importantly, a microscope's job is to put the image "very far" away, so that you can view it with a relaxed eye (it takes more effort to focus on something close to your face). Also, angular magnification is typically relevant for compont optical instruments, where the comparison is made when the object is measured from the objective lens and the angle of the image is measured at the focal point of the eyepiece.

 

[jix]

How about this: parallel light rays, makng a small angle α with the optical axis of a spherical concave mirror, where will the rays focus? First of all, do they focus on the same plane (perpendicular to the optical axis) as the focal point, and secondly, how far from the axis?

That's the actual question, but I wanted to get a better understanding of the concept as a whole.

 

[turin]

parallel light rays, makng a small angle α with the optical axis of a spherical concave mirror, where will the rays focus? First of all, do they focus on the same plane (perpendicular to the optical axis) as the focal point, and secondly, ...

I believe that they will, if α is small. That explains the small angle qualification.

... how far from the axis?

That's something that you should search in your book/notes, and then get back to us.