The work is dedicated to creating lenses for electro-optical Earth remote sensing systems. Optical systems for both visible and infrared spectral ranges are considered, and new calculation methods are proposed for them. High-resolution visible spectrum optical systems of spaceborne electro-optical systems require the use of lenses with large focal lengths, making them either mirror or mirror-lens systems. Among mirror lenses, three-mirror lenses without shielding and with an off-axis slit field of view and corrected distortion are of interest. The calculation of such a lens is investigated, and a simplified calculation methodology is proposed. A modification of the three-mirror anastigmatic Korsh's lens is also considered. Empirical formulas for the lens's design parameters have been obtained, allowing for the construction of a long-focus lens that corrects all five third-order aberrations (spherical aberration, coma, astigmatism, field curvature, and distortion). Unlike the Korsh's lens, to correct distortion, the magnification of the third mirror should be less than −2x. A method for designing thermally stable achromatic infrared three-component optical systems with simultaneous aberration minimization has been developed. Using this method, a lens for an infrared scanner consisting of three types of glass (IKS-25, zinc selenide, and germanium) was calculated and manufactured. The lens has a focal length of 112 mm, a relative aperture of 1:1, and can operate without thermal defocusing in a temperature range from −10 °C to + 50 °C.