试题与答案

内表面只反射而不吸收光的圆筒内有半径为R的黑球,距球心2R处有一点光源S,球心O

题型:计算题

题目:

内表面只反射而不吸收光的圆筒内有半径为R的黑球,距球心2R处有一点光源S,球心O和光源S皆在圆筒轴线上,如图所示.若使点光源向右半边发出的光最后全被黑球吸收,则筒的内半径r最大为多少?

答案:

 R

自S作球的切线SM,并画出S经管壁反射形成的虚像点S′,及由S′画出球面的切线S′N,如图甲所示,由图可看出,只要S′M和S′N之间有一夹角,则筒壁对从S向右的光线的反射光线就有一部分进入球的右方,不会完全落在球上被吸收.

由图可看出,如果r的大小恰能使S′N与S′M重合,如图乙所示,则r就是题目所要求的筒的内半径的最大值.这时SM与S′N的交点到球心的距离MO就是所要求的筒的半径r.由图乙可得

r=

由几何关系可知

sinθ=R/2R②

由①②式得r=R.

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题型:阅读理解

One night, as Diaz stepped off the train and onto a nearly empty platform, a teenage boy approached and pulled out a knife.

“He wanted my money, so I just gave him my wallet and told him, ‘Here you go ’” Diaz says.

As the teen began to walk away, Diaz told him, “Hey, wait a minute. You forgot something. If you’re going to be robbing people for the rest of the night, you might as well take my coat to keep you warm.”

The robber looked at him puzzled, saying, “Why are you doing this?”

Diaz replied, “If you’re willing to risk your freedom for a few dollars, then you must really need the money. I mean, all I wanted to do was get dinner and if you really want to join me…..”

Diaz says he and the teen went into a diner and sat in a booth.

“The manager comes by, the dishwashers come by, the waiters come by to say hi,” Diaz says.

The kid said, “You know everybody here. Do you own this place?”

“No, I just eat here a lot,” Dias said. “But you’re even nice to the dishwasher,” he said.

Diaz replied, “Well, haven’t you been taught you should be nice to everybody?”

“Yea, but I didn’t think people actually behaved that way,” the teen said.

When the bill arrived, Diaz said, “You’re going to have to pay for this bill because you have my money and I can’t pay for this. So if you give me my wallet back, I’ll gladly treat you.”

The teen returned it immediately. “I gave him $20…. I figure maybe it’ll help him.” Diaz says he asked for something in return--- the teen’s knife--- “and he gave it to me.”

Afterwards, when Diaz told his mother what happened, she said, “You’re the type of kid that if someone asked you for the time, you gave them your watch.”

“I figure, you know, if you treat people right, you can only hope that they treat you right. It’s as simple as it gets in this complicated world.”

小题1:What did Diaz do to the teen?

A.He gave the teen a new wallet

B.He treated the teen to dinner

C.He gave his coat to the teen

D.He taught the teen a lesson小题2:From the passage we can infer that the boy _______.

A.expressed his gratitude for Diaz’s kindness

B.gave up the idea of robbing in the end

C.wasn’t taught how to be nice to everybody

D.gave the knife to Diaz in return for his forgiveness小题3:For what Diaz did, his mother showed an attitude of _______.

A.complaint

B.concern

C.criticism

D.praise小题4:By telling the story of Diaz, the author intends to tell us ______.

A.to keep calm in danger

B.not to go out alone at night

C.to treat others kindly

D.not to harm others on purpose

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