Selection of active galactic nuclei (AGN) in the infrared allows the discovery of AGN whose optical emission is extinguished by dust. In this paper, we use the Spitzer Space Telescope First Look Survey (FLS) to assess what fraction of AGN with mid-infrared luminosities comparable to quasars are missed in optical quasar surveys due to dust obscuration. We begin by using the Sloan Digital Sky Survey (SDSS) database to identify 54 quasars within the 4 deg^2 extragalactic FLS. These quasars occupy a distinct region in mid-infrared color space by virtue of their strong, red, continua. This has allowed us to define a mid-infrared color criterion for selecting AGN candidates. About 2000 FLS objects have colors consistent with them being AGN, but most are much fainter in the mid-infrared than the SDSS quasars, which typically have 8 micron flux densities, S(8.0), ~1 mJy. We have investigated the properties of the 43 objects with S(8.0) >= 1 mJy satisfying our AGN color selection. This sample should contain both unobscured quasars, and AGN which are absent from the SDSS survey due to extinction in the optical. After removing 16 known quasars, three probable normal quasars, and eight spurious or confused objects from the initial sample of 43, we are left with 16 objects which are likely to be obscured quasars or luminous Seyfert-2 galaxies. This suggests the numbers of obscured and unobscured AGN are similar in samples selected in the mid-infrared at S(8.0)~1 mJy.
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