Bilingual edition: English is preserved and Chinese follows each unit. Terminology uses the confirmed v20260916 glossary; automated semantic review remains traceable.
中英双语版:英文原文完整保留,中文紧随对应单元;术语采用 v20260916 确认表,自动语义审校结果可追溯。

Lens-Maker's Formula

透镜公式

For a thin lens, the power is approximately the sum of the surface powers.

The radii of curvature here are measured according to the Cartesian sign convention. For a double convex lens the radius R1 is positive since it is measured from the front surface and extends right to the center of curvature. The radius R2 is negative since it extends left from the second surface.

这里的曲率半径是根据笛卡尔符号约定测量的。对于双凸透镜,R₁是正的,因为它是从前表面测量的,并延伸到中心曲率点。而R₂是负的,因为它是从第二表面向左延伸的。
For a lens in air which has index of refraction n =
对于在空气中折射率为n的透镜,
中文译文中的待填/计算数值依次对应:1:nl。实际数值以上方原输入框为准。
with surface radii R1 = cm and R2 = cm
表面半径 R 1 = cm 和 R 2 = cm
中文译文中的待填/计算数值依次对应:1:r1 2:r2。实际数值以上方原输入框为准。
the thin lens approximation of the power is P = diopters
薄透镜近似下,功率为 P = 象限
中文译文中的待填/计算数值依次对应:1:p。实际数值以上方原输入框为准。
which corresponds to focal length f = cm .
这对应于焦距 f = cm。
中文译文中的待填/计算数值依次对应:1:f。实际数值以上方原输入框为准。

If the lens is in another medium, such as water, its lens strength will be diminished.

如果透镜处于另一种介质中,例如水中,其透镜强度会减弱。
If the lens is in a medium of index n =
如果透镜位于折射率为n的介质中,
中文译文中的待填/计算数值依次对应:1:n2。实际数值以上方原输入框为准。
then the lens power will be diopters
那么透镜的功率将是屈光度
中文译文中的待填/计算数值依次对应:1:p2。实际数值以上方原输入框为准。
and the corresponding focal length f = cm.
以及相应的焦距 f = 厘米。
中文译文中的待填/计算数值依次对应:1:f2。实际数值以上方原输入框为准。

The above calculation is a single purpose calculation which returns the powers and focal lengths based on the values of the radii and indices of refraction. Substitute a number in any field and the calculation will be initiated. Default values will be entered for any unspecified parameter, but the index and radius values may be changed.

上述计算是一个单用途计算,根据曲率半径和折射率的值返回功率和焦距。在任何字段中输入一个数字,计算将被启动。未指定的参数将使用默认值,但索引和半径值可以更改。

The second part of the calculation above shows the diminshed power of a lens in a medium other than air. This gives important insight into the role of the two lenses of the human eye. The cornea has the greatest power because light enters it from the air. The inner crystalline lens has much less refractive power because it is suspended in a water-like medium.

上述计算的第二部分显示,当介质不是空气时,透镜的功率会减小。这为理解人眼两个透镜的作用提供了重要见解。角膜具有最大的功率,因为光线是从空气进入角膜的。而内晶状体的折射功率则要小得多,因为它悬浮在类似水的介质中。

For thick lenses , Gullstrand's equation can be used to calculate the lens power.

对于厚透镜,可以使用Gullstrand方程来计算透镜的功率。
对于薄透镜,其功率近似等于两个表面的功率之和。
Index

Lens concepts
棱镜概念索引
 
HyperPhysics***** Light and Vision
HyperPhysics ***** 光与视觉
R Nave
Go Back
返回