Magnification - Birth

Japanese: 倍率 - ばいりつ

The ratio of the size of an image to the size of an object. Various magnifications are defined depending on what quantity is considered as size. The lateral magnification is taken as the length of an object and its image perpendicular to the optical axis of the optical system, while the longitudinal magnification is taken as the length of an object and its image in the direction of the optical axis. Considering a single ray of light that leaves an object point on the optical axis and passes through an image point, and the angle that this ray makes with the optical axis on the object side and image side, this is the angular magnification. Simply speaking, magnification means lateral magnification. In general, magnification changes depending on the position of the object. The lateral magnification m of a spherical mirror or thin lens is equal to the ratio of s ', s , the distance from the vertex of the mirror or the center of the lens to the image point and the object point, respectively. In other words, m = ± s '/ s
Here, positive and negative are positive for lenses and negative for spherical mirrors, and when m is negative, the image is inverted. The magnification of a plane mirror is shown in Figure A , the magnification of a spherical mirror in Figure B , and the magnification of a lens in Figure C.

The magnification of optical instruments used with the naked eye, such as telescopes and microscopes, is sometimes defined as the ratio of the angle (visual angle) that an image seen through the optical instrument subtends at the center of the eye's pupil to the visual angle that the object subtends directly at the center of the eye's pupil without passing through the optical instrument. This is a ratio of angles, but not an angular magnification. The distance to the object and image is set to 250 mm, the distance of clear vision, when both are at infinity or a finite distance. If the focal lengths of the objective lens and eyepiece are f _o and f _e , respectively, the magnification of a telescope is f _o / f _e , and the magnification of a microscope is given by 250 Δ / ( f _o f _e ), where Δ is the optical tube length.

[Kazuo Miyake]

[Reference] | Microscope | Telescope | Lens

Magnification of a plane mirror (Figure A)
©Shogakukan ">

Magnification of a plane mirror (Figure A)

Magnification of spherical mirror (Figure B)
©Shogakukan ">

Magnification of spherical mirror (Figure B)

Lens magnification (Figure C)
©Shogakukan ">

Lens magnification (Figure C)

Source: Shogakukan Encyclopedia Nipponica About Encyclopedia Nipponica Information | Legend

Japanese:

像の大きさと物体の大きさの比。大きさとしてどんな量を考えるかで、種々の倍率が定義される。光学系の光軸に垂直な物体とその像の長さをとれば横倍率、光軸方向の物体とその像の長さをとれば縦倍率となる。光軸上の物点から出て像点を通る1本の光線を考え、この光線が物体側および像側で光軸となす角を考えたときが角倍率である。単に倍率といえば横倍率を意味する。一般に倍率は物体の位置によって変化する。球面鏡や薄いレンズの横倍率mは、それぞれ鏡の頂点またはレンズの中心からの像点、物点までの距離s'、sの比に等しい。すなわち
　　m＝±s'/s
で与えられる。ここで、正負は、レンズのときを正、球面鏡のときを負とし、mが負のときは倒立像となる。平面鏡の倍率を図A、球面鏡の倍率を図B、レンズの倍率を図Cに示す。

　肉眼で使用される望遠鏡、顕微鏡のような光学器械の倍率は、光学器械を通して見える像が目の瞳孔(どうこう)中心において張る角（視角）と、光学器械を通さずに物体が直接肉眼の瞳孔中心において張る視角の比により定義されることがある。これは、角度の比であっても角倍率ではない。物体および像までの距離としては、いずれも無限遠または有限距離のときには明視の距離250ミリメートルにとる。対物レンズと接眼レンズの焦点距離をそれぞれf_o、f_eとすると、望遠鏡の倍率はf_o/f_eで、顕微鏡の倍率は、光学的筒長をΔとすると、250・Δ/(f_of_e)で与えられる。