A new type of cloak is introduced that makes cloaked objects appear as a flat conducting sheet. This cloak avoids singular parameters and can be isotropic, making broadband optical cloaking more feasible. Transformation optics, which uses coordinate transformations, enables invisibility by making objects appear smaller. However, three topological cases exist: crushing to a point, line, or sheet. The sheet case is more practical as it avoids singularities. Metamaterials are typically used for transformation optics, but this study shows that isotropic dielectrics can be used instead, reducing absorption and enabling broadband cloaking. The cloak mimics a flat ground plane, avoiding scattering from the object. A coordinate transformation maps a virtual system to a physical system, minimizing anisotropy. The quasiconformal map is optimal for this, ensuring minimal anisotropy and a constant aspect ratio for transformed cells. This allows the cloak to be constructed using isotropic materials, simplifying fabrication. The cloak is tested with a Gaussian beam at 750 nm, showing that the cloak effectively mimics a flat ground plane, reflecting the beam without distortion. The cloak works across a wide frequency range due to low dispersion in dielectrics. A time-domain test shows that the cloak maintains the beam's shape after reflection, demonstrating effective cloaking. The study concludes that this approach is valid for both geometrical and wave optics, and the quasiconformal map is a versatile technique for transformation optics applications. The work is supported by the Croucher Foundation fellowship.A new type of cloak is introduced that makes cloaked objects appear as a flat conducting sheet. This cloak avoids singular parameters and can be isotropic, making broadband optical cloaking more feasible. Transformation optics, which uses coordinate transformations, enables invisibility by making objects appear smaller. However, three topological cases exist: crushing to a point, line, or sheet. The sheet case is more practical as it avoids singularities. Metamaterials are typically used for transformation optics, but this study shows that isotropic dielectrics can be used instead, reducing absorption and enabling broadband cloaking. The cloak mimics a flat ground plane, avoiding scattering from the object. A coordinate transformation maps a virtual system to a physical system, minimizing anisotropy. The quasiconformal map is optimal for this, ensuring minimal anisotropy and a constant aspect ratio for transformed cells. This allows the cloak to be constructed using isotropic materials, simplifying fabrication. The cloak is tested with a Gaussian beam at 750 nm, showing that the cloak effectively mimics a flat ground plane, reflecting the beam without distortion. The cloak works across a wide frequency range due to low dispersion in dielectrics. A time-domain test shows that the cloak maintains the beam's shape after reflection, demonstrating effective cloaking. The study concludes that this approach is valid for both geometrical and wave optics, and the quasiconformal map is a versatile technique for transformation optics applications. The work is supported by the Croucher Foundation fellowship.