Convert from feet [international, U.S.] to gnat's eye

Unit Definition (feet [international, U.S.])
The human foot has long been a standard unit for the measurement of length. Over history this size has varied from region to region and there is some discrepancy as to an exact standard or origin of the standard measurement for feet that we use today. In England, the Roman foot was replaced after the fall of Rome by the natural foot. The modern foot (1/3 yard or about 30.48 centimeters) did not appear until after the Norman conquest of 1066. It may be an innovation of Henry I, who reigned from 1100 to 1135. Later in the 1100's a foot of modern length, the "foot of St. Paul's," was inscribed on the base of a column of St. Paul's Church in London.

Unit Definition (gnat's eye)
The gnat's eye is an idiomatic "unit" of distance; it's common to hear that something is "as small as a gnat's eye". In fact, the eyes of typical gnats tend to have diameters similar in size to a hair's breadth: roughly 100-150 micrometers (0.10-0.15 millimeters).