In an adjustable light, a mounting base is formed with a pair of arcuate slots for receiving hooks protruding from a light module. For attachment of the light module to the base, the hooks enter open ends of the respective slots, and the light module is rotated to engage the hooks with the slots. A sheet of spring metal with two series of protrusions is sandwiched between a rear part of the base and a front part in which the slots are formed. The protrusions are exposed through the slots, and a space is provided behind the protrusions, allowing them to move resiliently when engaged by the hooks as the light module is rotated so that the light module can be retained in any selected one of a plurality of angular positions.