Does Placing a Second Lens at the Focal Point of the First Affect Magnification?

[KBriggs]

Homework Statement

Consider a positive thin lens L1. Using a ray diagram, show that if a second thin lense L2 is placed at the focal point of L1, the magnification does not change.

Homework Equations

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The Attempt at a Solution

First of all, the magnification does not change relative to what? Do they mean that the image will be the same size as if L2 was not there? Or does it mean that the magnification will be identically 1?

Either way, I drew a ray diagram for the case of an object outside the focal point of L1, using 2cm for both L2 and L1 focal lenghts. I drew a ray parallel to the optical axis into L1, which them goes to the focal point of L1 = the centre of L2, and therefore is undeviated by L2. The second ray I drew was through the focal point of L1, which emerges from L1 parallel to the optical axis, and therefore goes through the focal point of L2. The intersection gave the image, which neither had a magnification of 1, nor was it the same size as the image formed by L1 alone.

So, am I misinterpreting the question, or using the wrong rays, or what?

 

[Jhero]

Thank you for your question. The statement about the magnification not changing refers to the image size being the same as if L2 was not there. This means that the magnification will be 1, as the image size is equal to the object size.

To show this using a ray diagram, we can consider the two extreme cases: an object placed at infinity and an object placed at the focal point of L1.

1. Object at infinity: In this case, the rays from the object are parallel to each other and to the optical axis. These rays will pass through the focal point of L1 and emerge from L1 parallel to the optical axis. Since L2 is placed at the focal point of L1, the rays will pass through L2 undeviated and form an image at infinity. This image will be the same size as if L2 was not there, and hence the magnification will be 1.

2. Object at the focal point of L1: In this case, the rays from the object will be parallel to each other and will pass through the focal point of L1. These rays will emerge from L1 parallel to the optical axis and will pass through L2 undeviated. Since the object is at the focal point of L1, the image will also be at the focal point of L2, and hence the image size will be the same as the object size. Therefore, the magnification will again be 1.

In both cases, we can see that the magnification is 1, and hence the image size is the same as if L2 was not there. This shows that the placement of L2 at the focal point of L1 does not change the magnification.

I hope this explanation clarifies your doubts. If you have any further questions, please feel free to ask.

Scientist