An illuminating device comprising a light source and an optical element including a light receiving surface faced to a light emitting surface of the light source, a first light exit surface located opposite to the end of the optical element from the light receiving surface and a second light exit surface connecting the light receiving surface and the first light exit surface, wherein when the center of the light emitting surface is designated as a first point, a point at the edge of the light emitting surface is designated as a second point and an axis which passes through the first point and is perpendicular to the light emitting surface is designated as an optical axis, the first light exit surface of the optical element has a hollow around the optical axis with respect to the edge and in a cross section of the optical element including the optical axis and the second point, in an area at which angle of view from the first point with respect to the optical axis is from 25 degrees to 60 degrees, the first light exit surface has an area inclination of which is equal to or less than 20 degrees with respect to a straight line connecting the first point and the second point and when a point on the first exit surface at which angle of view from the first point with respect to the optical axis is 15 degrees is designated as a third point, an intersection of a ray which has been emitted at the second point and travels in parallel to the optical axis and the first light exit surface is designated as a fourth point, angle of incidence to the first light exit surface of a ray which has been emitted at the first point and reaches the third point is designated as θ 13, angle of incidence to the first light exit surface of a ray which has been emitted at the second point and reaches the third point is designated as θ 23, angle of incidence to the first light exit surface of a ray which has been emitted at the first point and reaches the fourth point is designated as θ 14, angle of incidence to the first light exit surface of a ray which has been emitted at the second point and reaches the fourth point is designated as θ 24, and the critical angle is designated as θ c, an area of the light emitting surface is represented as A, and a depth of the hollow on the first light exit surface is represented as E, the following conditions are satisfied, 15 ° ≤ θ 13 − θ 23 ≤ 70 ° 15 ° ≤ θ 14 − θ 24 ≤ 65 ° 0.2 ≤ θ 14 − θ 24 / θ 13 − θ 23 ≤ 1 θ c ≤ θ 13 θ 23 ≤ θ c 1 ≤ E / A / π ≤ 3 wherein in the cross section of the optical element including the optical axis and the second point, when an axis connecting the first point and the second point is designated as x axis, the first light exit surface is formed in such a way that all of light emitted at the first point undergoes total internal reflection in an area in which x coordinate of a point is equal to or greater than x coordinate of the third point, wherein in the cross section of the optical element including the optical axis and the second point, when an axis connecting the first point and the second point is designated as x axis, an area between the third point and the fourth point in x axis direction of the first light exit surface is formed in such a way that all of light emitted at the second point undergoes refraction, wherein in the cross section of the optical element including the optical axis and the second point, when an axis connecting the first point and the second point is designated as x axis, an area between the third point and the fourth point in x axis direction of the first light exit surface is on the other side of a straight line connecting the third point and the fourth point from the light source, and wherein the optical element is of infinite fold rotational symmetry around the optical axis. wherein in the cross section of the optical element including the optical axis and the second point, when an axis connecting the first point and the second point is designated as x axis, the first light exit surface is formed in such a way that all of light emitted at the first point undergoes total internal reflection in an area in which x coordinate of a point is equal to or greater than x coordinate of the third point, wherein in the cross section of the optical element including the optical axis and the second point, when an axis connecting the first point and the second point is designated as x axis, an area between the third point and the fourth point in x axis direction of the first light exit surface is formed in such a way that all of light emitted at the second point undergoes refraction, wherein in the cross section of the optical element including the optical axis and the second point, when an axis connecting the first point and the second point is designated as x axis, an area between the third point and the fourth point in x axis direction of the first light exit surface is on the other side of a straight line connecting the third point and the fourth point from the light source, and wherein the optical element is of infinite fold rotational symmetry around the optical axis.