Optical measuring apparatus is constructed to irradiate near infrared light to a desired portion, such as a head, of a person to be measured, receive arriving light from the desired portion and acquire information about a predetermined substance present in the desired portion on the basis of analysis of data related to the received arriving light. Measuring unit of the apparatus is provided on a cover member removably attachable to the person, and includes at least one light irradiation section for irradiating the near infrared light to the desired portion and at least one light reception section for receiving the arriving light from the desired portion. In a state where the cover member is attached to the person, the light irradiation and reception sections are positioned out of contact with the desired portion.