Optical designs for the Rosetta narrow-angle camera (NAC) and its UV spectrograph are presented. The NAC requires a 600 mm focal length system of focal ratio f/7 imaging a square field of width 2.3 deg onto a square detector array 2048 pixels wide. A cartographic method has been used to search for flat-field, three-mirror anastigmats (TMA) with the required geometrical constraints and at least one spherical surface; the use of spherical surfaces reduces fabrication cost and complexity and facilitates alignment. Two such systems are described, one with a spherical secondary, the other with a spherical tertiary. A deterministic alignment method is outlined where alignment defects are calculated from measurements of image position and Zernike wavefront coefficients. For the spectrograph, an all-reflecting, Thevenin-type concentric spectrograph has been designed. This design offers excellent image quality both spectrally and spatially along a long slit and it is compact and easily accommodated.