The problem of the detection and localization of a dielectric slab under a multifrequency plane-wave illumination is addressed. A linear inversion scheme, based on delta-functions, whose support represents the positions of the two slab interfaces, and on the truncated singular-value decomposition is exploited. The closed-form derivation of the amplitude of the reconstruction at the slab interface positions when the inversion scheme acts on exact model data allows us to analyze by means of analytical results the role played by the parameters of the slab, the frequency bandwidth, and the noise on the achievable probability of detection.