# 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.

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