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如图所示，截面为直角三角形ABC，∠B=30°，斜边AB=a．棱镜材料的折射率为n=

2
．在此截面所在的平面内，一条光线在距A点为a/8处的M点垂直AC射入棱镜，不考虑光线沿原路返回的情况，光线从玻璃砖的BC边射出．求：

（1）光从棱镜第一次射出时的折射角；

（2）光从棱镜第一次射出时的射出点与B点间的距离．

答案

（1）设玻璃砖的临界角为C．则有sinC=

1
n
=
1
2

得：C=45°

由几何知识知：光线在AB面上的入射角 i1=60°＞C，所以光线在AB上发生全反射．

根据反射定律和几何关系得知光线在BC面上的入射角 i2=30°＜C，可知光线将从BC面上射出玻璃砖．

设光从棱镜第一次射出时的折射角为r2．

则有：n=

sinr2
sini2

得：sinr2=nsini2=

2
×sin30°=
2
2
，

r2=45°．

（2）根据几何知识得：AD=

AM
cos60°
=2AM=
a
4

BD=AB-AD=a-

a
4
=
3
4
a

故EB=

1
2
BD
cos30°
=
1
2
×
3
4
a
3
3
=
3
4
a

答：（1）光从棱镜第一次射出时的折射角是45°；

（2）光从棱镜第一次射出时的射出点与B点间的距离是

3
4
a．

解答题

附加题：不等式2≤x2+mx+10≤6有且只有一个解，求实数m的值．
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单项选择题

阅读下列短文，从每题所给的四个选项(A、B、C和D)中，选出最佳选项，并在答题卡上将该项涂黑。

C

Reading can be a social activity. Think of the people who belong to book groups. They choose books to read and then meet to discuss them. Now, the website BookCrossing.com turns the page on the traditional idea of a book group.

Members go on the site and register the books they own and would like to share. BookCrossing provides an identification number to stick inside the book. Then the person leaves it in a public place, hoping that the book will have an adventure, traveling far and wide with each new reader who finds it.

Bruce Pederson, the managing director of BookCrossing, says, “The two things that change your life are the people you meet and books you read. BookCrossing combines both.”

Members leave books on park benches and buses, in train stations and coffee shops. Whoever finds their book will go to the site and record where they found it.

People who find a book can also leave a journal entry describing what they thought of it. E-mails are then sent to the BookCrossing to keep them updated about where their books have been found. Bruce peterson says the idea is for people not to be selfish by keeping a book to gather dust on a shelf at home. zxx.k

BookCrossing is part of a trend among people who want to get back to the “real” and not the virtual(虚拟). The site now has more than one million members in more than one hundred thirty-five countries.

What does the underlined word “it” in Paragraph 2refer to?（）

A.The book.

B.An adventure.

C.A public place.

D. The identification number.
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