问题 计算题

半径为R的半圆柱形玻璃砖,横截面如图1所示,O为圆心.已知玻璃的折射率为.一束与MN平面成450的平行光束射到玻璃砖的半圆柱面上,经玻璃折射后,有部分光能从MN平面上射出.

(1)求能从MN平面射出的光束的宽度为多少?

(2)如果平行光束是以45°角从空气射到半圆柱的平面表面上,如图2所示,设此时从半圆柱面上出射光束的位置与圆心O的连线跟MO夹角为φ,试求φ的范围.

答案

(1)(2)

(1) 图1-1中,BO为沿半径方向入射的光线,在O点正好发生全反射,           ---------(1分)

入射光线③在C点与球面相切,此时入射角,折射角为r,则有

 

即                   ---------(2分)

这表示在C点折射的光线将垂直MN射出,与MN相交于E点。MN面上OE即是出射光的宽度。                    ---------(1分)

        ---------(1分)

(2)如图1-2所示,由折身定律

,     ---------(1分)

如果光线EA刚好在A点发生全反射,则有

,而

即有                 ---------(1分)   

此时<EOA=75°                ---------(1分)

因EA与OB平行,所以

如果光线FC刚好在C点发生全反射,则有

          --------(1分)

此时            ---------(1分)

故知能够从半圆柱球面上出射的光束范围限制在AC区域上,对应的角度为               ---------(1分)

本题考查全反射发生的条件和光路图的画法,先画出光路图,再根据几何关系求得

选择题
阅读理解

E  

Many children first learn the value of money by receiving an allowance. The purpose is to let children learn from experience at an age when financial mistakes are not very costly.

The amount of money that parents give to their children to spend as they wish differs from family to family. Timing is another consideration. Some children get a weekly allowance. Others get a monthly allowance.

In any case, parents should make clear what, if anything, the child is expected to pay for with the money. At first, young children may spend all of their allowance soon after they receive it. If they do this, they will learn the hard way that spending must be done within a budget. Parents are usually advised not to offer more money until the next allowance.

The object is to show young people that a budget demands choices between spending and saving. Older children may be responsible enough to save money for larger costs, like clothing or electronics. Many people who have written on the subject of allowances say it is not a good idea to pay your child for work around the home. These jobs are a normal part of family life.

Paying children to do extra work around the house, however, can be useful. It can even provide an understanding of how a business works.

Allowances give children a chance to experience the three things they can do with money. They can share it in the form of gifts or giving to a good cause. They can spend it by buying things they want. Or they can save it.

Saving helps children understand that costly goals require sacrifice: you have to cut costs and plan for the future. Requiring children to save part of their allowance can also open the door to future saving and investing. Many banks offer services to help children and teenagers learn about personal finance. A savings account is an excellent way to learn about the power of compound interest.

Compounding works by paying interest on interest. So, for example, one dollar invested at two percent interest for two years will earn two cents in the first year. The second year, the money will earn two percent of one dollar and two cents, and so on. That may not seem like a lot. But over time it adds up.

77.For children who receive allowances, they’d better not ________.  

A. waste money to buy gifts for their parents or friends  

B. buy their favorite clothing or electronics for themselves  

C. save money like their parents or other adults  

D. ask for the next allowance before the decided date.

78.Many parents give children an allowance regularly to ______.  

A. meet children’s basic need for life       

B. give control over their children  

C. see whether they have financial mistakes  

D. help children learn how to manage money

79.If children are required to save their allowance, they ______.  

A. can experience three things related to money  

B. can understand the relation between goals and sacrifice  

C. will do more work around the house  

D. help themselves found the basis for their future life

80. What is the best title for the passage?

A. Be Generous to Pay Your Children

B. Be Wise to Avoid Financial Mistakes

C. Saving Allowances Does Good to Children

D. Allowances Help Children Learn about Money