Finding the magnification of a ball lens

[DharshanT]

Homework Statement

How to find the magnification of a ball lens?

Relevant Equations

Please see image below.

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.

 

[Charles Link]

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.

 

[rude man]

What happens if you Just use the lensmaker's formula. That would give you focal length and magnification.

 

[Charles Link]

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.

 

[rude man]

I think this one is best worked from first principles. The lensmaker's formula is for a thin lens.

oh yeh - good point