An endoscope illuminating optical system having a gradient index lens
capable of illuminating by a sufficient light amount and by a wider angle
is provided. The endoscope illuminating optical system is constituted to
illuminate an observed region by light guided by a light guide 1, by way
of a gradient index lens 2, and the gradient index lens 2 satisfies
Condition Equations (2) and (3) below: (AR).sup.2.ltoreq.0.6 (2)
0.5k+0.35.ltoreq.AL/.pi..ltoreq.0.5k+0.65 (3) where, R designates an
effective radius of the gradient index lens, L designates a length in an
optical axis X direction of the gradient index lens, A designates a
constant coefficient, k designates a nonnegative integer.