Finding the magnification of a ball lens

In summary, the conversation discusses the effective and back focal lengths for magnification purposes, referencing a literature review that suggests a lens of 1mm diameter can have a magnification of 350x-400x. The calculations behind this are not fully understood and the conversation suggests taking a point off-axis and computing the magnified angle using parallel rays. The magnification formula is also mentioned, referencing a 10" or 25cm reference point, and the suggestion to use the lensmaker's formula for focal length and magnification is brought up. However, it is noted that first principles may be the best approach for this situation.
  • #1
DharshanT
1
0
Homework Statement
How to find the magnification of a ball lens?
Relevant Equations
Please see image below.
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I don't really know how to relate the effective and back focal lengths for magnification purposes. Literature review suggests that a lens of 1mm diameter can have a magnification of 350x-400x, but I don't really know the calculations behind it. Please advise.
 
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  • #2
I believe you need to take a point off-axis an distance ## d ## in the focal plane and compute the ## \Delta \theta_{magnified} ## for the parallel rays that emerge. The magnification is often referenced to 10" or about 25 cm, if I'm not mistaken, so that magnification ## M=\frac{ \Delta \theta_{magnified}}{d/(10")} ##. ## \\ ## In more detail: ## \\ ## Without the ball, the eye sees an object of size ## d ## subtending an angular spread of ## \Delta \theta_{unmagnified}=\frac{d}{10"} ##. ## \\ ## When viewed with the ball, the angular spread will be ## \Delta \theta_{magnified} ##= whatever you compute by putting the object as a point in the focal plane off-axis by a distance ## d ##. ## \\ ## The ratio of these two angles, ## M=\frac{\Delta \theta_{magnified}}{\Delta \theta_{unmagnified}} ##, is the magnification.
 
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  • #3
What happens if you Just use the lensmaker's formula. That would give you focal length and magnification.
 
  • #4
rude man said:
What happens if you Just use the lensmaker's formula. That would give you focal length and magnification.
I think this one is best worked from first principles. The lensmaker's formula is for a thin lens.
 
  • #5
Charles Link said:
I think this one is best worked from first principles. The lensmaker's formula is for a thin lens.
oh yeh - good point
 
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Likes Charles Link

Related to Finding the magnification of a ball lens

What is a ball lens?

A ball lens is a small spherical lens made from a transparent material such as glass or plastic. It is used in optical systems to focus or collimate light.

How do I find the magnification of a ball lens?

To find the magnification of a ball lens, you first need to know the focal length of the lens. Then, you can use the formula: magnification = image distance / object distance. The image distance is the distance between the lens and the image formed, while the object distance is the distance between the lens and the object being viewed.

What factors affect the magnification of a ball lens?

The magnification of a ball lens is primarily affected by the focal length of the lens. Longer focal lengths result in higher magnification, while shorter focal lengths result in lower magnification. Other factors that can affect magnification include the curvature and size of the lens, as well as the refractive index of the material it is made from.

Can I use a ball lens to magnify images in both directions?

Yes, a ball lens can magnify images in both directions. When an object is placed in front of the lens, it will appear larger when viewed through the lens. Similarly, when an object is placed behind the lens, it will appear smaller when viewed through the lens.

What are some common applications of ball lenses?

Ball lenses have a variety of applications in fields such as microscopy, fiber optics, and laser technology. They are commonly used to focus or collimate light in optical systems, as well as in imaging and sensing applications. They can also be used in medical devices, cameras, and telescopes.

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