 Solution

The hemispherical component needs 100.0 eV electrons, whereas electrons arrive at its entrance optics with 111.4 eV. The optics must therefore remove 11.4 eV, requiring a retarding-potential magnitude of 11.4 V. For a negative electron, moving to a more negative electrostatic potential increases potential energy, so the retarding region is 11.4 V negative relative to the analyser entrance. Equivalently the hemisphere entrance is 11.8 V negative relative to the sample vacuum reference after including the 0.4 V contact step. Reporting 11.8 V as the additional instrument retardation would count the contact correction twice.