What separation distance will make the combination of a +3.00 and a +10.00 thin lens afocal?

To determine the separation distance that will make the combination of a +3.00 D and a +10.00 D lens afocal, one needs to consider how lenses combine optically. An afocal system occurs when the focal lengths of the lenses are arranged in such a way that they cancel out one another's power.

In this case, the combined focal length (F) of two thin lenses placed in contact can be calculated using the lensmaker’s formula:

F = (f1 * f2) / (f1 + f2)

However, when the lenses are separated by a distance (d), the condition for afocality is that the distance d between the lenses equals the absolute value of the focal length of the first lens (f1) added to the focal length of the second lens (f2). In this case, the focal lengths of the +3.00 D and +10.00 D lenses are:

• f1 = 1 / +3.00 = 0.333 m (or 33.3 cm)

• f2 = 1 / +10.00 = 0.1 m (or 10 cm)

To achieve afocality, the separation distance must equal