1. An image processing device comprising: a memory; and a processor coupled to the memory, configured to: acquire, by a camera, an image of a face of a user facing a direction different from a direction of the camera, determine whether or not the user is wearing glasses based on the acquired image, when determining whether or not the user is wearing glasses, extracting a first contour position indicating a contour position of the face that appears without glasses and extracting a second contour position indicating a contour position of the face that appears through the glasses, from the acquired image, determine that the glasses are farsighted glasses when the first contour position is further from a center of the face than the second contour position, determine that the glasses are nearsighted glasses when the second contour position is further from the center of the face than the first contour position, specify a first straight line from a camera position of the camera to a refraction point on a lens of the glasses from the camera position to the second contour position, specify a second straight line from a center position of a cross section of the face to the second contour position, specify an intersection of the first straight line and the second straight line, calculate a distance between the second contour position and the intersection, finalize a process executed by the processor when the calculated distance is smaller than a threshold value defined beforehand, and when the calculated distance is greater than the threshold value, determine a refraction index for the glasses based on the threshold value.