The exposure of a path p is a measure of the likelihood that an object traveling along p is detected by a network of sensors and it is formally defined as an integral over all points x of p of the sensibility (the strength of the signal coming from x) times the element of path length. The minimum exposure path (MEP) problem is, given a pair of points x and y inside a sensor field, find a path between x and y of a minimum exposure. In this paper we introduce the first rigorous treatment of the problem, designing an approximation algorithm for the MEP problem with guaranteed performance characteristics. Given a convex polygon P of size n with O(n) sensors inside it and any real number ε> 0 , our algorithm finds a path in P whose exposure is within an 1 + ε factor of the exposure of the MEP, in time O(n/ε ² ψ), where ψ is a topological characteristic of the field. We also describe a framework for a faster implementation of our algorithm, which reduces the time by a factor of approximately Θ(1/ε), by keeping the same approximation ratio.