问题 计算题

【选修3-4选做题】

有一种高脚酒杯(脚高且细),如图所示,杯内底面为一凸起的球面,球心在顶点O下方玻璃中的C点,球面的半径为R=1.50cm,O点到杯口平面的距离为8.0cm,在杯脚底中心处P点紧贴一张小画片,P点距O点6.3cm.这种酒杯未斟酒水,若在杯口上方向杯底方向观看,看不出画片上的景物.已知玻璃的折射率n=1.56,角度很小时,可以认为sinα=α。求:   

(1)光在玻璃中的传播速度;    

(2)计算画片成像位置离杯口的距离.

答案

解:(1)  

(2)把酒杯放平,分析成像问题,未斟酒时,杯底凸球面的两侧介质的折射率分别为。在图中,P为画片中心,由P发出经过球心C的光线PO经过顶点不变方向进入空气中;由P发出的与PO成角的另一光线PAA处折射。设A处入射角为i,折射角为r,半径CAPO的夹有为θ,由折射定律和几何关系可得

  

在△PAC中,由正弦定理,有

考虑近轴光线成像,都是小角度,则有

由(2)(4)(5)式、的数值及,可得

  

由(6)(7)式有

由上式及图可知,折射线将与PO延长线相交于即为P点的实像,画面将成实像于

在△中,由正弦定理有

又有

考虑到是近轴光线,由(9)(10)式可得

又有

由以上各式并代入数据,可得

所以像离杯口的距离为0.1cm

写作题

第二节读写任务(共1小题,满分25分)

阅读下面的短文,然后按照要求写一篇150词左右的英语短文。

The generation gap between students and teachers is becoming more significant with only 3.3 percent out of a survey group of 1,000 students from 30 key middle schools in the city saying they would be willing to tell their teachers of their inner thoughts.

In today’s educational environment, teachers are positioned to be the authority figure for learning instead of also becoming good friends in the life of students.

As only students with good marks in exams are considered the “ apples in the eyes” of the teachers, most students think their teachers to be partial (偏心).

“ I feel sad to hear such remarks”, said Yu Yi , a well-known special-class teacher.

She recalled that in the past, teachers and students would play basketball together or comment on the novels while sitting on the grass during a break. But today, study and good marks are the only topics of conversation between students and teachers.

“Schools are not only the place where knowledge is imparted (传授) but also where students are taught how to be an upright person,” Yu said. “The success of a person is not merely determined by intelligence but also by emotional state. ”

Yang Xiong, director of the Juvenile Research Institute, said the educational system which focuses on examinations should be held to be substantially responsible.

[写作内容]

1. 以约30个词概括学生不愿告诉老师内心想法的原因;

2. 以约120个词就“现代师生关系”这个主题发表你的看法,包括如下要点:

( 1 ) 你是否愿意告诉老师你内心的想法,为什么?

( 2 ) 你希望你与你的老师之间的关系是怎样的,如何才能建立这种关系?

[写作要求]

1. 可以使用实例或其他论述方法支持你的论点,也可以参照阅读材料的内容,但不得直接引用原文中的句子;2. 标题自定;3. 文中不能出现考生真实姓名和学校名称。

[评分标准]    概括准确,语言规范,内容合适,篇章连贯。

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