Convex 镜像

播放段落

Convex mirrors provide a wide angle view and they provide an upright image. Wide angle images have benefits in rearview , in-store customer monitors, and for viewing large areas like intersections and parking lots.
::剖面镜提供了宽广的视角视图,提供了直立的图像。 广角图像有利于后视、内层客户监视器,也有利于查看十字路口和停车场等大片地区。

播放段落

Images in a Convex Mirror
::在 Convex 镜像中的图像

播放段落

In  convex mirrors , the reflecting surface is on the outside of the sphere, making the center of curvature and the focal point on the opposite side of the mirror from the object. Since the focal point is on the opposite side of the mirror from the object, the focal length is assigned a negative number.
::在光线镜中,反射面在球体外面,使弯曲中心和镜面与对象对面的焦点。由于焦点在镜面对面,焦距被设定为负数。

播放段落

Light rays that come to the mirror aimed at the focal point on the back side will be reflected parallel to the principal axis . In the sketch, blue rays approach the mirror as if they would continue through the mirror toward the focal point (dotted blue lines). They reflect along the purple lines parallel to the principal axis.
::照镜子的光线,瞄准后侧的焦点,将与主轴平行反射。在草图中,蓝色射线接近镜子,仿佛通过镜子向着焦点(点形蓝色线)继续前进。它们沿着主轴平行的紫线反射。

播放段落

Similarly, light rays that approach the mirror parallel to the principal axis reflect as if they came from the focal point.
::同样,接近与主轴平行的镜子的光线也反映出它们似乎来自联络点。

播放段落

Example
::示例示例示例示例

播放段落

A  convex mirror has a radius of curvature of 40.0 cm. If the object is 1000.0 cm, find the image distance and the magnification.
::二次曲线镜的半径为40.0厘米。如果对象为1000.0厘米,请找到图像距离和放大度。

播放段落

  $\begin{array}{r}\frac{1}{d_o}+\frac{1}{d_i}=\frac{1}{f}\end{array}$   so  $\begin{array}{r}\frac{1}{1000.}+\frac{1}{x}=\frac{1}{-20.0}\end{array}$
::1do+1di=1f so 11000.+1x=1-20.0

播放段落

Multiplying both sides by $\begin{array}{r}1000x\end{array}$  yields $\begin{array}{r}x+1000=-50x\end{array}$  and $\begin{array}{r}51x=-1000\end{array}$  and $\begin{array}{r}x=-19.6\text{ cm}\end{array}$ .
::将两边乘以 1000x 产量 x+100050x 和 51x1000 和 x19.6 cm 。

播放段落

Since the image distance is negative, it means the image is behind the mirror and is virtual. The image will be upright.
::由于图像距离为负, 这意味着图像在镜子后面, 是虚拟的。 图像将直立 。

播放段落

::mdido(-19.6)1000=0.0196或151

播放段落

The image is reduced by a factor of 51.
::图像减少51倍。

播放段落

For a convex mirror, if the object is at infinity, the image will be a dot on the focal point. As the object moves from infinity toward the mirror, the image moves along the principal axis toward the mirror. When the object right next to the mirror, the image will be right next to the mirror on the other side.
::对于卷尾镜来说,如果对象在无限度,图像将是焦点上的点。当对象从无限度向镜子移动时,图像沿着主轴向镜子移动。当对象在镜子旁边时,图像将紧靠另一侧的镜子。

播放段落

All ray diagrams for convex mirrors look essentially like the image below, with the placement of the image somewhere between the mirror and the focal point.
::直角镜像的所有射线图都与下面的图像基本相似,图像位于镜像和焦点之间的某处。

播放段落

The ray tracing for convex mirrors follow this general sketch. Two rays leave the tip of the object, one approaches the mirror parallel and reflects as if it came from the focal point. The top blue dotted line shows this imaginary route. The second ray leaves the object tip and approaches the mirror toward the focal point but reflects parallel at the mirror. The green solid line shows the reflected ray and the dotted green line shows the imaginary route behind the mirror. Where the two dotted lines intersect is the tip of the image. All images in convex mirrors are upright, virtual, and diminished. As the object moves toward the mirror, the image also moves toward the mirror and increases in size. This can be determined using the mirror and magnification equations.
::曲线镜的射线跟踪跟踪跟随这个一般草图。 两条射线留下对象的端, 一向镜面平行, 反射的边缘, 并像从焦点一样。 上蓝色点线显示这个假想路线 。 第二条射线离开对象端, 朝镜面朝着焦点, 反射镜面反射。 绿色固线显示反射线, 虚绿线则显示镜子后面的假想路线 。 两条虚线是图像的端口 。 光线镜中的所有图像都是直立、 虚拟和缩小的 。 随着对象向镜面移动, 图像也向镜面移动, 并增加其大小 。 这可以通过镜面和放大方程式来确定 。

播放段落

When light enters a Cassegrain telescope from a distant planet, first it bounces off a concave primary mirror and then off a secondary convex mirror. Play around with a Cassegrain telescope in the simulation below and see if you can until you get a clear view of Jupiter in the eyepiece:
::当光从遥远的行星进入卡塞克雷纳望远镜时, 它首先从一个凝固的主镜上反弹, 然后从一个二次的孔面镜上反弹。 在下面的模拟中, 与卡塞克雷纳望远镜一起玩耍, 看看能否在眼睛上看到木星的清晰视图 :

播放段落

Summary
::摘要

播放段落
• For convex mirrors, the reflecting surface is on the outside of the sphere, placing the center of curvature and the focal point on the opposite side of the mirror from the object.
  ::对于卷尾镜来说,反射表面位于球体外部,将弯曲中心和焦点置于物体反射镜的对面。
播放段落
• Light rays that approach the mirror aimed at the focal point will be reflected parallel to the principal axis.
  ::接近照点镜的光线将反映与主轴平行的光线。
播放段落
• Light rays that come to the mirror parallel to the principal axis reflect as if they came from the focal point.
  ::射向镜面的光线与主轴平行,反射成像来自联络点。
播放段落
• Since the focal point is on the opposite side of the mirror from the object, the focal length is assigned a negative number.
  ::由于协调人位于对象反射镜的对面,因此对协调人的长度设定了负数。
播放段落
• Both the mirror equation and the magnification equation are true with convex mirrors.
  ::镜像方程式和放大方程式 与阴道镜像是真实的

播放段落

Review
::回顾

播放段落
1. Find the image distance of an object placed 5.00 cm in front of a convex mirror whose focal length is 8.00 cm.
   ::查找一个物体的图像距离,该物体将5.00厘米放置在焦距为8.00厘米的卷轴镜面前。
播放段落
2. Find the image distance of an object placed 3.00 cm in front of a convex mirror whose focal length is 8.00 cm.
   ::查找一个物体的图像距离,该物体将3.00厘米放置在焦距为8.00厘米的方形镜像前。
播放段落
3. A 4.0 cm tall light bulb is placed a distance 35.5 cm from a convex mirror with a focal length of -12.2 cm.
   播放段落
   1. Find the image distance.
      ::寻找图像距离 。
   播放段落
   2. Find the image size.
      ::查找图像大小 。
   
   ::A4.0厘米高的光灯灯泡在离光镜35.5厘米的距离处放置,焦距为-12.2厘米。 查找图像距离。 查找图像大小 。

播放段落

Explore More
::探索更多

播放段落

Use this resource to answer the questions that follow.
::使用此资源回答下面的问题 。

 

播放段落
1. Images in a convex mirror are always ___________ and always ___________.
   ::光线镜中的图像总是... . . . . . . . . .
播放段落
2. The image in a convex mirror will always be on the ___________ (same or opposite) side of the mirror from the object.
   ::光线镜中的图像将始终位于对象的镜子的...(相同或对面)一侧。