The relationship between aperture focal length and depth of field is not in the field of photography, but in the field of applied optics

These two statements are not contradictory, but they are both correct.

First, the aperture number f is directly proportional to the depth of field, and the focal length is inversely proportional to the depth of field. It means that when taking pictures, the greater the F value, the smaller the aperture and the greater the depth of field of the photos taken. This is why the F value of landscape photos should be adjusted above 7 if the depth of field is large. The focal length is inversely proportional to the depth of field, which means the same aperture and the same shooting distance. When shooting with lenses with different focal lengths, such as 35mm, 50mm, 100mm and 200mm, or with different focal lengths of zoom lenses, the lens with large focal length (telephoto) has a deep scene and the lens with small focal length (wide angle) has a large depth of field.

Second, F * D = F'? (The aperture number f multiplied by the entrance pupil diameter d equals the focal length f') means that when designing and manufacturing lenses, the maximum aperture is different when manufacturing lenses with different focal lengths with the same aperture (that is, D). For example, a 35mm lens with F 1.4 has a maximum aperture of F 1.4. If the technical parameters such as lens aperture and aperture opening are kept unchanged, a 50mm lens is made, and its maximum aperture value is 1.4 * 50/35 = F2.0 ... This can be understood by a triangular relationship. After the focal moment of the lens changes, the angle of view formed by the light entering the lens at the focal point is inversely proportional to the focal moment under the same aperture opening. To help you understand, I drew you a simple schematic diagram.