Abstract: A surgical instrument in particular for eye surgery has a housing having a good surface for placement on the eye. A knife is held retracted within the housing under the bias of a torsion spring. An ultra-sonic transducer measures the thickness of the part of the eye local to the surface. A control system responds to the measured thickness to displace the knife to project from the surface by an amount related to the depth.In this way where an incision is effected it can be ensured that the depth of the incision never exceeds the depth of that part of the eye being incised.