Diffusing member, illuminating device, image reading apparatus, and image forming apparatus to improve diffusivity of light with suppressing a decrease of incident light on an illuminated region of an original

An illuminating device comprising a diffusing surface with a plurality of protruding portions arrayed in a first direction,

• wherein the plurality of protruding portions includes a first group of protruding portions, tops of the first group of protruding portions being arranged on a first line parallel to the first direction when the first group of protruding portions are projected on a first cross section parallel to the first direction, and
• wherein the following conditions are satisfied:
• 1.5≤β/α≤35
• 0≤γ/β≤0.5
• where α, β and γ represent frequencies of inclination angles of the first group of protruding portions within a range of 0°±5°, a range of
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• respectively, at respective positions on a predetermined line n parallel to the first direction of the first group of protruding portions when the first group of protruding portions are projected on a second cross section including each top of the first group of protruding portions and perpendicular to the first cross section, ω represents a radiation angle of light incident on the diffusing surface, and n represents a refractive index of the illuminating device;
• at least one light source;
• a light guiding body formed of transparent optical material and having an incident surface and an exit surface, the light guiding body configured to guide light emitted from the at least one light source;
• and
• a diffusing member configured to diffuse the light guided by the light guiding body toward an irradiated surface,
• wherein the incident surface is a surface on which the light from the at least one light source is incident, and the exit surface is a surface from which the light from the incident surface exits toward the irradiated surface, and
• wherein the light guiding body and the diffusing member are integrated with each other such that the diffusing surface of the diffusing member serves as the exit surface of the light guiding body;
• and
• based on the diffusivity of the light exiting from the exit surface by a diffusing structure formed on the exit surface of the light guiding body and an availability efficiency of light in the light guiding body satisfying the conditions, the diffusivity of a light amount improves and the decrease in the light amount of the light exiting from the exit surface is suppressed.