# Calculating minimum object distance for a lens

I am trying to figure out the Minimum Object Distance based on a simulation available here.

In case you can't open it (it's a Java applet...) I'll describe it briefly. It shows an object emitting light rays which go through 2 positive thin lenses. You can move around both the object and the lens that is further away from it. There are some questions that the user is supposed to answer. It's in French, by the way.

The second question there asks what condition has to be met for the object to remain focused. I thought that, for starters, the object should be at least at the Minimum Object Distance from the lens, so I tried to calculate it like this:

First, I calculate the focal length: $$\frac{1}{b} + \frac{1}{g} = \frac{1}{f}$$ where b is the distance to the image, g is the distance to the object and f is the focal length.

I am assuming that b is the distance between the rightmost lens (the one further away from the object, the one through which rays exit) and the point where the rays converge.

I am also assuming that g is the distance between the leftmost lens (the one closer to the object, the one through which rays enter) and the object itself.

Is that right?

After that, I calculate the MOD like this: $$MOD = \frac{f\cdot b} {b-f}$$ The thing is that, no matter how I change the values, MOD is always equal to g. This does not make sense at all. Shouldn't the MOD be always the same regardless of the position of the object?

I am completely new to this, so I'm sure that I must be making an obvious mistake.

## 1 Answer

Well the short answer, is that there is NO minimum object distance for a lens. The object distance can be anywhere from - infinity to - 0 .

I assume you are using the normal left to right convention, so all object distances are negative. And if you are not assuming "thin lenses" the you really are in trouble.

For object distances from - infinity, to - f , the image will move from + f to + infinity.

For object distances from - f to - 0 , the image will be virtual

• With Minimum Object Distance I'm referring to the minimum distance at which the image will be focused. Therefore, even though the object can of course be anywhere, isn't there such a concept as Minimum Object Distance? Cameras indeed cannot focus objects that are too close, and I think I've seen photography discussions mentioning this concept. – cangrejo Jun 25 '13 at 9:00
• Well a camera lens will focus the IMAGE of an OBJECT at infinity, at a distance approximately f from the lens. If the OBJECT moves towards the lens, the IMAGE moves further away from the lens, so you have to refocus, by moving the film or sensor further back. when the OBJECT is a distance 2f from the lens, the IMAGE has moved to 2f from the lens, That is the smallest OBJECT to IMAGE distance 4f, with a magnification of -1 – user26165 Jun 26 '13 at 20:06