Ray Diagrams for Lenses

The image formed by a single lens can be located and sized with three principal rays. Examples are given for converging and diverging lenses and for the cases where the object is inside and outside the principal focal length.

The "three principal rays" which are used for visualizing the image location and size are:

1. A ray from the top of the object proceeding parallel to the centerline perpendicular to the lens. Beyond the lens, it will pass through the principal focal point. For a negative lens, it will proceed from the lens as if it emanated from the focal point on the near side of the lens.
   从物体顶部发出的一条光线，方向平行于透镜的中心线且垂直于透镜。在透镜之后，它将通过主焦点。对于凹透镜，它会从透镜发出，仿佛是从透镜近侧的焦点发出。
2. A ray through the center of the lens, which will be undeflected. (Actually, it will be jogged downward on the near side of the lens and back up on the exit side of the lens, but the resulting slight offset is neglected for thin lenses.)
   通过透镜中心的光线，将不会被偏转。（实际上，它会在透镜的近侧向下偏移，然后在远侧向上偏移，但这种轻微的偏移对于薄透镜来说被忽略。）
3. A ray through the principal focal point on the near side of the lens. It will proceed parallel to the centerline upon exit from the lens. The third ray is not really needed, since the first two locate the image.
   通过透镜近侧主焦点的光线。在透镜另一侧射出时，它将平行于中心线传播。第三条光线其实并不需要，因为前两条光线已经确定了像的位置。

Ray Diagrams for Convex Lenses

For an object outside the focal point, a real inverted image will be formed. 对于位于焦点以外的物体，会形成一个实像，且像为倒立的。

For an object inside the focal point, a virtual erect image will be formed. 对于位于焦点内的物体，会形成一个虚像，且像为直立的。

Ray Diagrams for Concave Lenses

The ray diagrams for concave lenses inside and outside the focal point give similar results: an erect virtual image smaller than the object. The image is always formed inside the focal length of the lens.

Ray Diagram for Two Lenses