ZP_Salon

Remark#2: Formula of Image Location:

Formula of an image location of a lens: When an object is located at a in front of a lens with a focal length f, an image of the object is produced at b behind the lens. The relation among a, b, and f is a formula of an image location and is given as

In the case of a glass lens this formula is called as Gaussian lens formula. When an image B’B of an object AA’ is produced by a lens the formula is proved easily from the geometrical relation between the light rays A’RB’ and A’OB’ as follows (see Fig.1).

In this proof we utilized a feature of a lens that a ray A’R which is in parallel to the optical axis is deflected at the lens and proceeds to the focal point as RFB’, and a ray passing through the center of the lens is not deflected at the center of the lens O’ and goes straight as A’OB’.

Fig.1 Explanatory diagram for proving the formula of image location of a lens.

Formula of an image location of a zone plate: In the case of a zone plate, too, the same formula of an image location holds. But it should be noticed that the ground for the formula is different. The ground of the formula for a zone plate is that the path length from the point A to the point B via the n-th zone is longer than that via the central zone by (n/2) times the wavelength (see Fig.2). The red and green lines show cases of finite a and infinite a, respectively. This is expressed as