Understanding Converging Lenses: Question on Image Size

[dioprem]

Homework Statement

This is the given question. The blue rays represent the solution.
http://img16.imageshack.us/img16/7237/lenstq.jpg

Homework Equations

None.

The Attempt at a Solution

The blue rays are essentially my solutions, but only up to the point where the rays are reflected off the mirror. The rays after hitting the lens after that are from my teacher. Once they hit the lens, I know the 2 rays need to converge at a point along the focal plane, since the rays are parallel. What I want to know is why is the image the same size as the object?

 

[CWatters]

Try drawing rays from other points on the needle such a point Y.

 

[BBAI BBAI]

CWatters is right. Rays from X and Y are parallel.

 

[dioprem]

@CWatters The problem is the solution requires me to only draw to rays from point X. So I cannot draw addition rays from point X or any other rays from any other point of the needle. Only 2 rays from X are allowed. So I don't understand why the image is the same size as the object.

 

[mfb]

Consider a third ray from X which hits M right in the middle (you don't have to draw it). It is symmetric around the optical axis, and it has to hit the same point as the other two rays. Y is projected on itself. Therefore, the image of (XY) has the same size as (XY).

 

[Basic_Physics]

magnification = - image distance/object distance

 

[dioprem]

Thank you mfb and Basic_Physics. Answered my question!