radius of curvature

简明释义

曲率半径

英英释义

例句

1.To calculate the bending of light, one must know the radius of curvature 曲率半径 of the lens.

要计算光的弯曲，必须知道镜头的曲率半径 radius of curvature。

2.In road design, engineers must consider the radius of curvature 曲率半径 to ensure safe turning.

在道路设计中，工程师必须考虑曲率半径 radius of curvature以确保安全转弯。

3.The radius of curvature 曲率半径 of the Earth can be approximated in various geographic calculations.

地球的曲率半径 radius of curvature可以在各种地理计算中近似。

4.The formula for the lens curvature is based on the radius of curvature 曲率半径 of the lens surface.

镜头的曲率公式是基于镜头表面的曲率半径 radius of curvature。

5.The radius of curvature 曲率半径 of a spherical mirror affects its focal length.

球面镜的曲率半径 radius of curvature会影响其焦距。

作文

The concept of the radius of curvature is fundamental in various fields of science and engineering, particularly in geometry and optics. The radius of curvature refers to the radius of a circular arc that best approximates a curve at a given point. This measurement is critical for understanding how light behaves when it passes through lenses or reflects off mirrors. In essence, it helps us to quantify the degree of curvature of a surface, which can have significant implications in practical applications.In geometry, the radius of curvature provides insights into the properties of curves. For example, a circle has a constant radius of curvature equal to its radius, while more complex shapes like parabolas or hyperbolas have varying radii of curvature along their lengths. The tighter the curve, the smaller the radius of curvature, indicating a sharper turn. Conversely, a gentle curve will have a larger radius of curvature. This principle is not only applicable to theoretical mathematics but also plays a crucial role in real-world scenarios such as road design, where engineers must consider the radius of curvature to ensure safety and comfort for drivers.In optics, the radius of curvature is vital for designing lenses and mirrors. For instance, a convex lens has two surfaces, each with its own radius of curvature. The relationship between the radius of curvature and the focal length of the lens is expressed by the lens maker's equation, which allows optical engineers to create lenses that focus light accurately. Similarly, in the case of concave mirrors, the radius of curvature determines how well the mirror can concentrate light to form images. A smaller radius of curvature in mirrors results in a more powerful convergence of light rays, which is essential in applications like telescopes and satellite dishes.Moreover, the radius of curvature has significant implications in fields like physics and biology. In physics, understanding the radius of curvature is crucial when analyzing the motion of objects along curved paths, such as in roller coasters or planetary orbits. The concept also appears in biology when studying the shapes of cells and organisms, where the radius of curvature can influence growth patterns and structural stability.In conclusion, the radius of curvature is a versatile concept that transcends various disciplines. Its importance in geometry, optics, and even biology highlights the interconnectedness of different fields of study. By understanding the radius of curvature, we gain valuable insights into the behavior of curves and surfaces, enabling us to design safer roads, create effective optical devices, and comprehend natural forms. As technology continues to advance, the applications of the radius of curvature will undoubtedly expand, leading to further innovations and discoveries across multiple domains.

“曲率半径”这一概念在科学和工程的多个领域中都是基础，特别是在几何学和光学中。“曲率半径”是指在给定点上最能近似曲线的圆弧的半径。这一测量对于理解光线在透镜中传播或反射在镜子上的行为至关重要。从本质上讲，它帮助我们量化表面的曲率程度，这在实际应用中可能具有重要意义。在几何学中，“曲率半径”提供了对曲线性质的洞察。例如，一个圆的“曲率半径”恒定，等于它的半径，而更复杂的形状如抛物线或双曲线在其长度上有不同的“曲率半径”。曲线越紧，曲率半径就越小，表示转弯越尖锐。相反，温和的曲线将具有更大的“曲率半径”。这一原理不仅适用于理论数学，还在现实世界的场景中发挥着至关重要的作用，例如道路设计，工程师必须考虑“曲率半径”，以确保驾驶者的安全和舒适。在光学中，“曲率半径”对于设计透镜和镜子至关重要。例如，凸透镜有两个表面，每个表面都有自己的“曲率半径”。透镜制造商方程式表达了“曲率半径”和透镜焦距之间的关系，这使得光学工程师能够制造出准确聚焦光线的透镜。同样，在凹面镜的情况下，“曲率半径”决定了镜子聚集光线形成图像的能力。较小的“曲率半径”会导致光线的更强聚合，这在望远镜和卫星天线等应用中是必不可少的。此外，“曲率半径”在物理学和生物学等领域也具有重要影响。在物理学中，理解“曲率半径”对于分析沿曲线路径运动的物体至关重要，例如过山车或行星轨道。该概念在生物学中也出现，当研究细胞和生物体的形状时，“曲率半径”可以影响生长模式和结构稳定性。总之，“曲率半径”是一个多功能的概念，跨越多个学科。它在几何学、光学甚至生物学中的重要性突显了不同研究领域之间的相互联系。通过理解“曲率半径”，我们获得了对曲线和表面行为的宝贵见解，使我们能够设计更安全的道路、创造有效的光学设备，并理解自然形式。随着技术的不断进步，“曲率半径”的应用无疑将扩展，导致多个领域进一步的创新和发现。