凸透镜标准不确定度的误差分析

2021-04-10 来源：爱站旅游

导读凸透镜标准不确定度的误差分析

凸透镜标准不确定度的误差分析

to clean and repair, it is strictly forbidden to head reaches into the mechanical stroke range. 17th article: in overhead transmission line following work should blackout, cannot blackout Shi, due isolation protection measures, crane shall not in overhead transmission line following work, through overhead transmission line should will lifting arm falls, in overhead line side work Shi, regardless of in any situation Xia, lifting arm, and rope or weights, and overhead transmission line of recently distance should not is less than Xia table provides: transmission line voltage 1000 v following 1-15 kV 20-40 kV 60-110 kV 220,000 v Allow minimum distances with the transmission line (m) vertical 1.5 level 1 1.5 2 3 4 5 6 4 6 18th: lamp voltage may not exceed 36 volts, when working in a damp place or metal containers, lamp voltage may not exceed 12 volts. 19th: pressure vessel should have a safety valve, pressure gauge, and avoid sun exposure, collisions, oxygen cylinders to prevent contaminated oil; of acetylene gas, LPG, must have a safety device to prevent tempering. 20th: x-ray and gamma-ray flaw detector operation area, non-operator, not allowed to enter. Article 21st: corrosion, dust and radioactive and toxic work, protective measures are required, and to carry out regular inspection. Spider-man 22nd section III: Spider-man to regular medical examinations of the medical diagnosis, who suffer from high blood pressure, heart disease, anemia, epilepsy and other discomfort in the Spider-man shall not engage in aerial work. 23rd: Spider-man dressed spirit, banned the wearing of

hard bottom and easy slip-on shoe nail. 24th: Spider-man material stack stationary, tools should turn into a tool bag, transfer prohibited throwing of objects. 25th: in case of bad weather (such as wind in the above grade) construction safety, prohibition of the open air, lifting and piling. 26th article: ladder shall not deficiency document, no padded using, ladder cross document spacing to 30 cm suitable, using Shi top to tied prison, bottom should take anti-sliding measures, single ladder and ground angle to 60 degrees suitable, ban II people while in ladder Shang job, as needed received long using, should lashing firm, people Word ladder in end of feet pulled prison, in channel at using ladder, due guardianship or set fence. 27th: no security measures, prohibited in hip joints, supports, trusses of the roof truss cantilever beams, and choose the frame and half fixed widget or job to walk on, Spider-man and the ground ... Nine, ten basic security to prevent vehicle damage claim 1, without legal training of qualified certified personnel not familiar with vehicle performance is not driving a car. 2, should insist on doing defense work, vehicle brake, Horn, steering systems, lighting and other safety components such as poor are not allowed out of the car. 3, dump truck, dump truck car hop is strictly prohibited, prohibited goods mixing, loading of vehicles should not overload,

凸透镜焦距的测定的误差分析

林明菊

摘要:透镜是光学仪器中最基本的光学元件～而透镜焦距是透镜的重要参量之一～透镜的成像位置及性质,大小、虚实,均与其有关。本文通过对凸透镜焦距测定的研究～在相同测量条件下采用两次成像法取不同的d、D值测得的结果进行比较分析～总结出D值的选取对不确定度影响的规律～为焦距测量实验提供一些数据参考。

关键词:薄透镜,凸透镜,焦距,测量方法,实验误差

不同透镜有不同的焦距，而同一透镜的焦距有多种测量方法，对于测量方法的选取应根据不同的透镜、不同的精度要求和具体的实验条件选择合适的方法。测量凸透镜焦距的方法主要有以下几种:物距像距法测凸透镜焦距、辅助透镜成像法测凸透镜焦距、两次成像法测凸透镜焦距(又称共轭法、贝塞尔法或位移法)、自准直法测凸透镜焦距等。笔者根据现有的实际情况及实验条件，对大学物理中常用的两次成像法，选取在各种物屏像屏距离D值(D,4f)的情况下测量凸透镜焦距，并通过不确定度分析总结出在相同条件下，如何选取合适的物屏像屏距离才能测得较精确结果的结论。

1(透镜基本知识

透镜是由两个折射面所限定的透明体组成称为透镜，是光学仪器中最基本的光学元件。薄透镜是透镜中最基本的一种，其厚度较自身球面的曲率半径及焦距要小得多，厚度可忽略不计。薄透镜可分为凸透镜和凹透镜。其中心厚度大于边

[1]缘厚度的称为凸透镜，中心厚度小于边缘厚度的称为凹透镜。

焦距是光学系统中衡量光的聚集或发散的度量参数，指从透镜的光心到光聚集之焦点

的距离，它是表征透镜成像性质的重要参数。

2. 测量值不确定度的意义

在物理测量中，测量的理想值是获得被测量在测量条件下的真值，但在实际的测量过程中由于实验方法、实验仪器和实验者操作技能等因素的影响，测量值只能是被测量的一个近似值，但它是在真实值附近的一个测量值范围内，测量不确定度就是评定此测量值范围的一个测量质量指标。若此量值范围越窄，即测量

[2]不确定度越小，则测量值表示真实值的可能性就越高。

cylinders to prevent contaminated oil; of acetylene gas, LPG, must have a safety device to prevent tempering. 20th: x-ray and gamma-ray flaw detector operation area, non-operator, not allowed to enter. Article 21st: corrosion, dust and radioactive and toxic work, protective measures are required, and to carry out regular inspection. Spider-man 22nd section III: Spider-man to regular medical examinations of the medical diagnosis, who suffer from high blood pressure, heart disease, anemia, epilepsy and other discomfort in the Spider-man shall not engage in aerial work. 23rd: Spider-man dressed spirit, banned the wearing of hard bottom and easy slip-on shoe nail. 24th: Spider-man material stack stationary, tools should turn into a tool bag, transfer prohibited throwing of objects. 25th: in case of bad weather (such as wind in the above grade) construction safety, prohibition of the open air, lifting and piling. 26th article: ladder shall not deficiency document, no padded using, ladder cross document spacing to 30 cm suitable, using Shi top to tied prison, bottom should take anti-sliding measures, single ladder and ground angle to 60 degrees suitable, ban II people while in ladder Shang job, as needed received long using, should lashing firm, people Word ladder in end of feet pulled prison, in channel at using ladder, due guardianship or set fence. 27th: no security measures, prohibited in hip joints, supports, trusses of the roof truss cantilever beams, and choose the frame and half fixed widget or job to walk on, Spider-man and the ground ... Nine, ten basic security to prevent vehicle damage claim 1, without legal training of qualified certified personnel not familiar with vehicle performance is not driving a car. 2, should insist on doing defense work, vehicle brake, Horn, steering systems,

lighting and other safety components such as poor are not allowed out of the car. 3, dump truck, dump truck car hop is strictly prohibited, prohibited goods mixing, loading of vehicles should not overload,

engage in aerial work. 23rd: Spider-man dressed spirit, banned the wearing of hard bottom and easy slip-on shoe nail. 24th: Spider-man material stack stationary, tools should turn into a tool bag, transfer prohibited throwing of objects. 25th: in case of bad weather (such as wind in the above grade) construction safety, prohibition of the open air, lifting and piling. 26th article: ladder shall not deficiency document, no padded using, ladder cross document spacing to 30 cm suitable, using Shi top to tied prison, bottom should take anti-sliding measures, single ladder and ground angle to 60 degrees suitable, ban II people while in ladder Shang job, as needed received long using, should lashing firm, people Word ladder in end of feet pulled prison, in channel at using ladder, due guardianship or set fence. 27th: no security measures, prohibited in hip joints, supports, trusses of the roof truss cantilever beams, and choose the frame and half fixed widget or job to walk on, Spider-man and the ground ... Nine, ten basic security to prevent vehicle damage claim 1, without legal training of qualified certified personnel not familiar with vehicle performance is not driving a car. 2, should insist on doing defense work, vehicle brake, Horn, steering systems, lighting and other safety components such as poor are not allowed out of the car. 3, dump truck, dump truck car hop is strictly prohibited, prohibited goods mixing, loading of vehicles should not overload,

由于测量值有误差，误差的来源不同对其测量值的影响也不同。总体来说物理实验测量的误差来源主要为两类，一类是偶然误差，另一类是系统误差(仪器引入的误差和实验方法引入的误差)。偶然误差是由重复测量产生偶然效应，使测量值分散而引入的，因此

用统计的方法评定标准不确定度，就是标准不确定度的A类评定;仪器引入的误差是由于仪器的影响，使测量值向某一方向有恒定的偏移而引入，因此用统计的方法评定标准不确定度，就是标准不确定度的B类评定。由于其测得值的不确定度来源不止一个，所以对于某物理量测定后，要计算测得值的不确定度，要合成其标准不确定度，即称为合成标准不确定度。在本文u,(f)中对凸透镜焦距的分为九组(每组测五次)进行测量后，分别求合成标准不确定度，用以探究与真实值最接近的一个焦距值范围。

3. 测凸透镜焦距所使用实验仪器

光具座是测量几何光学的重要实验仪器之一。它不仅造型美观、结构合理，而且使用灵活方便、经久耐用，是测量凸透镜焦距的必备仪器，尤其是导轨与滑座各附标尺，便于测量滑座平移的距离。它由导轨(用于盛放双面像屏、激光光源支架、弹性镜架等仪器器件)、滑座(调节滑座使其标尺零位对准导轨中央的凸棱，以此作为水平位的初始状态)、可调支架、弹性镜架、弹簧片架、弹簧片架、双面像屏、激光光源支架、延伸架、光源用开关电源、可调升降立柱、刻度载物平台等组成。

4. 两次成像法测量凸透镜焦距的实验原理

两次成像法测凸透镜焦距光路图如下图所示。设保持物屏与像屏的相对位置

'不变，并使其距离，当凸透镜置于物屏与像屏之间时，可以找到两个透镜D,4f

位置，像屏上都能得到清晰的像，如图所示。透镜两个位置(与)之间的距LL21

d离的绝对值为。运用物像的共轭对称性质，容易证明

22Dd,'f, 4D

L1 L2

\"PP

d'PD

两次成像法原理图

''dD只要测出和，就可以算出。由于是通过透镜两次成像而求得的，因ff

而此法又称为两次成像法。同时可以看出，成像时都是把透镜看成无限薄的，物距与像距都近似地用从透镜光心算起的距离来代替，而这种方法中则毋须考虑透l, should be removed

fixed,

demolition

work

restricted

area,

under

supervisedateriallowed to throw up or down the materials and tools and other objects. 10, the construction site, where a fall may be of any ml not be any chaos on the walkway placed or dropped down, keep working the aisles clear. 9, when working at height, are not ad shallition work is high, disassembly of the materials, construction waste should be cleaned up and removed in a timely manner, anight, all items should be stacked smooth, can not be placed in or near the hole, and not interfere with traffic. 8, when demoblocks, railings or other safety devices. 7,

when working at he-on the circumstances provided channel. 6, vacant jobs, should have a firm foothold and properly tie off belts field should be configured depending-the balcony, climbing and walking in the non nstruction workers should be provided for channel up and down, do not climb scaffolding, acrossheld equipment should be checked before use to ensure safe and secure. Edges of opening job preventing objects falling. 5, co-e correct. 4, various types of handmust bas not to slip in danger of falling. 3, in the climbing operations, structure must be solid and reliable climbing equipment, s, high heels, tools should turn into a tool bag. 2, high operating personnel is strictly prohibited to fight each other, so sliding shoe-from a height, object hit ten basic safety requirements 1, working at height must be neat, do not wear plastic bottom action and, when traction on ramps, a car and you were allowed to jobs and remain at the bottom. Ten, the prevention of fallseen trd not back down. 10, motor vehicles towing vehicle with no brakes, traction object objects shall not, shall not enter is betwock to obstruct traffic; avoid vehicle, should not avoid two car intersection, not dead standing next to the parking lot couland uneven rows of flshaped pieces of wood on either side of the wheel. 9, the presence of motor vehicles should avoid walking on the right side, -t. 8, when loading and unloading operation, if the vehicles parked on the ramp, it should be fixed with wedget nighrricades shall be set in the road safety labels, safety signs and protective measures, and to ensure that adequate lighting adestrians crowded locations and access door. 7, and scaffolding near the motorway operation area and other facilities, and babridges, forks road, slow pe speed\namely: road conditions

unknown to slow, bad line slowly, slower start, passing, parking, narrow roads, detours, road-row space should be free of command. 6, the site traffic comes into play to slow down and do it \"fournar avoid vehicles falls when you start braking. 5, and from the construction site, pitch turning, reversing, when driving in the unstable objects falling hurts. 4, take the vehicle in a safe place, head, hands and body shall not reveal the compartment to high and ultra wide strapping should be solid and reliable, should prevent the car-ultra 2

radioactive and toxic work, protective measures are required, and to carry out regular inspection. Spider-man 22nd section III: Spider-man to regular medical examinations of the medical diagnosis, who suffer from high blood pressure, heart disease, anemia, epilepsy and other discomfort in the Spider-man shall not engage in aerial work. 23rd: Spider-man dressed spirit, banned the wearing of hard bottom and easy slip-on shoe nail. 24th: Spider-man material stack stationary, tools should turn into a tool bag, transfer prohibited throwing of objects. 25th: in case of bad weather (such as wind in the above grade) construction safety, prohibition of the open air, lifting and piling. 26th article: ladder shall not deficiency document, no padded using, ladder cross document spacing to 30 cm suitable, using Shi top to tied prison, bottom should take anti-sliding measures, single ladder and ground angle to 60 degrees suitable, ban II people while in ladder Shang job, as needed received long using, should lashing firm, people Word ladder in end of feet pulled prison, in channel at using ladder, due guardianship or set fence. 27th: no security measures, prohibited in hip joints, supports, trusses of the roof truss cantilever beams, and choose the frame and half fixed widget or job to walk on, Spider-man and the ground ... Nine, ten basic security to prevent vehicle damage claim 1, without legal training of qualified certified personnel not familiar with vehicle performance is not driving a car. 2, should insist on doing defense work, vehicle brake, Horn, steering systems, lighting and other safety components such as poor are not allowed out of the car. 3, dump truck, dump truck car hop is strictly prohibited, prohibited goods mixing, loading of vehicles should not overload,

[3]镜本身的厚度。因此，用这种方法测出的焦距一般较为准确。 5. 测凸透镜焦距的实验方法

测凸透镜焦距首先要对光学系统进行共轴调节，其目的是使各透镜的光轴重合且与光具座的导轨严格平行，光线能通过各元件中心，将像呈现在像屏上，进而避免不必要的像差和使读数准确，共轴调节的有粗调和细调两个步骤。若在物屏、像屏、光源不变的情况下，移动凸透镜，两次成像的像中心位置不变，则可

[4]以判断出各元件已经共轴。

在共轴调节完成之后才能进行凸透镜焦距的测量，将物屏与像屏固定在相距

'大于的位置，测出它们之间的距离，但要注意的是测量物、透镜及像的位置D4f

时，要检查滑块上的读数准线和被测平面是否一致，如果不一致会导致误差，该实验是用T形辅助棒法去测，位置统一由辅助棒法所在滑块的准线去读，误差将

,会减小。再者人眼对成像的清晰度的分辨能力不是很强，因而像屏在一小范围,p内移动时，人眼所见的像是同样清晰的，此范围为深景。为了减少由此引入的误差，可由进向远和由远向近移动白屏，去探测像的位置，并取二位置的平均值为像的位置。如上图所示，移动透镜，使屏上得到清晰的物像，记录透镜的位置。移L1动透镜至另一位置，使屏上又得到清晰的物像，再记录透镜的位置，重复5次，L2求其平均值及标准不确定度，最后得出实验结果。改变屏的位置，测九组有效数据。

6(凸透镜焦距的测量数据及不确定度估算

6.1 第1组实验数据 (物屏位置P:17.30 cm 像屏位置P,:95.05 cm )

表1 单位:cm

f'次数凸透镜位置L1 凸透镜位置L2 二次成像透镜距离d 焦距

1 38.55 75.55 37.00 15.04

2 38.65 75.08 36.43 15.22

3 38.88 75.50 36.62 15.13

4 38.66 75.20 36.54 15.14

5 38.85 75.35 36.50 15.15

物屏像屏距离D1= 77.75 cm

不确定度计算及实验结果:

1d,d'平均值: ,1in

=(37.00+36.43+36.62+36.54+36.50)/5

=36.62 cm

1f',f'平均值: ,in

=(15.04+15.22+15.13+15.14+15.15)/5

=15.14 cm

ump truck car hop is strictly prohibited, prohibited goods mixing, loading of vehicles should not overload,uck, de brake, Horn, steering systems, lighting and other safety components such as poor are not allowed out of the car. 3, dump trertified personnel not familiar with vehicle performance is not driving a car. 2, should insist on doing defense work, vehiclman and the ground ... Nine, ten basic security to prevent vehicle damage claim 1, without legal training of qualified c-n, Spiderhip joints, supports, trusses of the roof truss cantilever beams, and choose the frame and half fixed widget or job to walk o ed inin end of feet pulled prison, in channel at using ladder, due guardianship or set fence. 27th: no security measures, prohibit ees suitable, ban II people while in ladder Shang job, as needed received long using, should lashing firm, people Word laddersliding measures, single ladder and ground angle to 60 degr-o 30 cm suitable, using Shi top to tied prison, bottom should take antiair, lifting and piling. 26th article:

ladder shall not deficiency document, no padded using, ladder cross document spacing tad weather (such as wind in the above grade) construction safety, prohibition of the open man material stack stationary, tools should turn into a tool bag, transfer prohibited throwing of objects. 25th: in case of b-on shoe nail. 24th: Spider-and easy slipman dressed spirit, banned the wearing of hard bottom -man shall not engage in aerial work. 23rd: Spider-discomfort in the Spider medical examinations of the medical diagnosis, who suffer from high blood pressure, heart disease, anemia, epilepsy and other man to regular-man 22nd section III: Spider-d, and to carry out regular inspection. Spideroperator, not allowed to enter. Article 21st: corrosion, dust and radioactive and toxic work, protective measures are require-ray flaw detector operation area, non-maray and gam-cylinders to prevent contaminated oil; of acetylene gas, LPG, must have a safety device to prevent tempering. 20th: x exceed 12 volts. 19th: pressure vessel should have a safety valve, pressure gauge, and avoid sun exposure, collisions, oxygen tage may not exceed 36 volts, when working in a damp place or metal containers, lamp voltage may not110 kV 220,000 v Allow minimum distances with the transmission line (m) vertical 1.5 level 1 1.5 2 3 4 5 6 4 6 18th: lamp vol-40 kV 60-15 kV 20-following 1 1000 vs, and overhead transmission line of recently distance should not is less than Xia table provides: transmission line voltage d will lifting arm falls, in overhead line side work Shi, regardless of in any situation Xia, lifting arm, and rope or weightshoul olation protection measures, crane shall not in overhead transmission line following work, through overhead transmission lineanical stroke range. 17th article: in overhead transmission line following work

should blackout, cannot blackout Shi, due isto clean and repair, it is strictly forbidden to head reaches into the mech 3

2，，d,d,iu, A()dn(n,1)

2222，，，0.380.190.080.12 ,20

=0.010

, u,B(d)3

0.10 =

=0.058

22u,u，u ABC()d

22 = 0.010，0.058

=0.059

2,,f,,2u,u ，，d,,,()fd,,

2,,d2,, = u，，d,,2D,,1

236.62，0.059,, = ,,2，77.75,,

=0.014

结果表述:f',f',u ,，，f

D1,2.123 =cm (15.14,0.014)d1

6.2 第2组实验数据(物屏位置P:17.30 cm 像屏位置P,:85.25 cm D=67.95cm ) 2

表2 单位:cm

f'次数凸透镜位置L1 凸透镜位置L2 二次成像透镜距离d 焦距 1 41.15 63.15 22.00 15.21 2 40.96 63.45 22.49 15.13 3 40.80 63.25 22.45 15.13 4 41.10 63.50 22.50 15.12 5 40.98 63.60 22.62 15.11

6.3 第3组实验数据(物屏位置P:17.30 cm 像屏位置P,:80.35 cm D=63.05 cm) 3

表3 单位:cm

f'次数凸透镜位置L1 凸透镜位置L2 二次成像透镜距离d 焦距 1 44.05 56.05 12.00 15.19 2 43.50 55.85 12.35 15.16 3 43.90 56.25 12.35 15.16 4 43.70 55.95 12.25 15.17 5 43.85 55.65 11.80 15.21

working at height, are not ad shallition work is high, disassembly of the materials, construction waste should be cleaned up and removed in a timely manner, anight, all items should be stacked smooth, can not be placed in or near the hole, and not interfere with traffic. 8, when demoblocks, railings or other safety devices. 7, when working at he-high and ultra wide strapping should be solid and reliable, should prevent the caron the circumstances provided channel. 6, vacant jobs, should have a firm foothold and properly tie off belts field should be configured depending-the balcony, climbing and walking in the non nstruction workers should be provided for channel up and down, do not climb scaffolding, acrossheld equipment should be checked before use to ensure safe and secure. Edges of opening job preventing objects falling. 5, co--e correct. 4, various types of handmust bas not to slip in danger of falling. 3, in the climbing operations, structure must be solid and reliable climbing equipment, s, high heels, tools should turn into a tool bag. 2, high operating personnel is strictly prohibited to fight each other, so sliding shoe-from a height, object hit ten basic safety requirements 1, working at height must be neat, do not wear plastic bottom action and, when traction on ramps, a car and you were allowed to jobs and remain at the bottom. Ten, the prevention of fallseen trultrad not back down. 10, motor vehicles towing vehicle with no brakes, traction object objects shall not, shall not enter is betwock to obstruct traffic; avoid vehicle, should not avoid two car intersection, not dead standing next to the parking lot couland uneven rows of flshaped pieces of wood on either side of the wheel. 9, the presence of motor vehicles should avoid walking on the right side, -t. 8, when loading and unloading

operation, if the vehicles parked on the ramp, it should be fixed with wedget nighrricades shall be set in the road safety labels, safety signs and protective measures, and to ensure that adequate lighting adestrians crowded locations and access door. 7, and scaffolding near the motorway operation area and other facilities, and babridges, forks road, slow pe speed\namely: road conditions unknown to slow, bad line slowly, slower start, passing, parking, narrow roads, detours, road-row space should be free of command. 6, the site traffic comes into play to slow down and do it \"fournar avoid vehicles falls when you start braking. 5, and from the construction site, pitch turning, reversing, when driving in the unstable objects falling hurts. 4, take the vehicle in a safe place, head, hands and body shall not reveal the compartment to 4

have a safety valve, pressure gauge, and avoid sun exposure, collisions, oxygen cylinders to prevent contaminated oil; of acetylene gas, LPG, must have a safety device to prevent tempering. 20th: x-ray and gamma-ray flaw detector operation area, non-operator, not allowed to enter. Article 21st: corrosion, dust and radioactive and toxic work, protective measures are required, and to carry out regular inspection. Spider-man 22nd section III: Spider-man to regular medical examinations of the medical diagnosis, who suffer from high blood pressure, heart disease, anemia, epilepsy and other discomfort in the Spider-man shall not engage in aerial work. 23rd: Spider-man dressed spirit, banned the wearing of hard bottom and easy slip-on shoe nail. 24th: Spider-man material stack stationary, tools should turn into a tool bag, transfer prohibited throwing of objects. 25th: in case of bad weather (such as wind in the above grade) construction safety, prohibition of the open air, lifting and piling. 26th article: ladder shall not deficiency document, no padded using, ladder cross document spacing to 30 cm suitable, using Shi top to tied prison, bottom should take anti-sliding measures, single ladder and ground angle to 60 degrees suitable, ban II people while in ladder Shang job, as needed received long using, should lashing firm, people Word ladder in end of feet pulled prison, in channel at using ladder, due guardianship or set fence. 27th: no security measures, prohibited in hip joints, supports, trusses of the roof truss cantilever beams, and choose the frame and half fixed widget or job to walk on, Spider-man and the ground ... Nine, ten basic security to prevent vehicle damage claim 1, without legal training of qualified certified personnel not familiar with vehicle performance is not driving a car. 2,

should insist on doing defense work, vehicle brake, Horn, steering systems, lighting and other safety components such as poor are not allowed out of the car. 3, dump truck, dump truck car hop is strictly prohibited, prohibited goods mixing, loading of vehicles should not overload,

6.4 第4组实验数据(物屏位置P:17.30 cm 像屏位置P,:90.25 cm D=72.95cm) 4

表4 单位:cm

凸透镜位置L1 凸透镜位置L2 二次成像透镜距离d f'次数焦距

1 39.85 70.05 30.20 15.11

2 39.75 70.00 30.25 15.10

3 39.80 69.85 30.05 15.14

4 39.75 70.10 30.35 15.08

5 39.79 69.95 30.11 15.13 6.5 第5组实验数据(物屏位置P:17.30 cm 像屏位置P,:77.20 cm D=59.90cm) 5

表5 单位:cm

凸透镜位置L1 凸透镜位置L2 二次成像透镜距离d f'次数焦距

1 45.65 50.60 4.95 14.87

2 47.10 50.35 3.25 14.93

3 4+.65 50.20 3.55 14.92

4 46.65 50.15 3.50 14.92

5 46.60 50.00 3.40 14.93 6.6 第6组实验数据(物屏位置P:17.30 cm 像屏位置P,:78.45 cm D=61.15cm) 6

表6 单位:cm

凸透镜位置L1 凸透镜位置L2 二次成像透镜距离d f'次数焦距

1 45.95 52.35 6.40 15.12

2 45.45 52.95 7.50 15.06

3 45.55 52.60 7.05 15.08

4 46.05 52.55 6.50 15.11

5 45.65 51.95 6.30 15.13 6.7 第7组实验数据(物屏位置P:17.30 cm 像屏位置P,:92.20 cm D=74.90cm ) 7

表7 单位:cm

凸透镜位置L1 凸透镜位置L2 二次成像透镜距离d f'次数焦距

1 39.15 72.75 33.60 14.96

2 39.40 72.80 33.40 15.00

3 39.25 72.80 33.55 14.97

4 39.20 72.75 33.55 14.97

5 39.25 72.70 33.45 14.99 6.8 第8组实验数据(物屏位置P:17.30 cm 像屏位置P,:101.00 cm D=83.70cm ) 8

表8 单位:cm

凸透镜位置L1 凸透镜位置L2 二次成像透镜距离d f'次数焦距

1 38.20 82.15 43.95 15.16

2 38.15 82.10 43.95 15.16

3 37.95 82.05 44.10 15.12

4 38.00 82.15 44.15 15.10

5 38.09 82.12 44.03 15.13

prohibition of the open man material stack stationary, tools should turn into a tool bag, transfer prohibited throwing of objects. 25th: in case of b-on shoe nail. 24th: Spider-and easy slipman dressed spirit, banned the wearing of hard bottom -man shall not engage in aerial work. 23rd: Spider-discomfort in the Spider medical examinations of the medical diagnosis, who suffer from high blood pressure, heart disease, anemia, epilepsy and other man to regular-man 22nd section III: Spider-d, and to carry out regular inspection. Spideroperator, not allowed to enter. Article 21st: corrosion, dust and radioactive and toxic work, protective measures are require-ray flaw detector operation area, non-maray and gam-cylinders to prevent contaminated oil; of acetylene gas, LPG, must have a safety device to prevent tempering. 20th: x exceed 12 volts. 19th: pressure vessel should have a safety valve, pressure gauge, and avoid sun exposure, collisions, oxygen tage may not exceed 36 volts, when working in a damp place or metal containers, lamp voltage may not110 kV 220,000 v Allow minimum distances with the transmission line (m) vertical 1.5 level 1 1.5 2 3 4 5 6 4 6 18th: lamp vol-40 kV 60-15 kV 20-following 1 1000 vs, and overhead transmission line of recently distance should not is less than Xia table provides: transmission line voltage d will lifting arm falls, in overhead line side work Shi, regardless of in any situation Xia, lifting arm, and rope or weightshoul olation protection measures, crane shall not in overhead transmission line following work, through overhead transmission lineanical stroke range. 17th article: in overhead transmission line following work should blackout, cannot blackout Shi, due isto clean and repair, it is strictly forbidden to head reaches into the mech 5

construction safety, prohibition of the open air, lifting and piling. 26th article: ladder shall not deficiency document, no padded using, ladder cross document spacing to 30 cm suitable, using Shi top to tied prison, bottom should take anti-sliding measures, single ladder and ground angle to 60 degrees suitable, ban II people while in ladder Shang job, as needed received long using, should lashing firm, people Word ladder in end of feet pulled prison, in channel at using ladder, due guardianship or set fence. 27th: no security measures, prohibited in hip joints, supports, trusses of the roof truss cantilever beams, and choose the frame and half fixed widget or job to walk on, Spider-man and the ground ... Nine, ten basic security to prevent vehicle damage claim 1, without legal training of qualified certified personnel not familiar with vehicle performance is not driving a car. 2, should insist on doing defense work, vehicle brake, Horn, steering systems, lighting and other safety components such as poor are not allowed out of the car. 3, dump truck, dump truck car hop is strictly prohibited, prohibited goods mixing, loading of vehicles should not overload,

6.9 第9组实验数据(物屏位置P:17.30 cm 像屏位置P,:79.20 cm D=61.90cm ) 9

表9 单位:cm

凸透镜位置L1 凸透镜位置L2 二次成像透镜距离d f'次数焦距

1 43.75 54.40 10.65 15.02

2 44.90 53.60 8.70 15.17

3 44.30 53.85 9.55 15.11

4 44.32 53.70 9.38 15.12

5 44.25 53.70 8.17 15.21

同理，第2组—第9组实验的数据处理、不确定度估算及实验结果与表1数据的处理方法相同，其结果见表10。

表10 单位:cm

组数物屏像屏uf'uduu D/ df'ABC,(d)(d)(d)(f)序号距离D

1 77.75 36.62 15.14 0.010 0.058 0.059 0.014 2.123 15.14,0.0142 67.95 22.41 15.14 0.011 0.058 0.059 0.010 3.032 15.14,0.0103 63.05 12.35 15.18 0.022 0.058 0.062 0.006 5.105 15.18,0.0064 72.95 30.19 15.01 0.001 0.058 0.058 0.012 2.416 15.11,0.0125 59.90 3.73 14.91 0.309 0.058 0.314 0.010 16.06 14.91,0.0106 61.15 6.75 15.10 0.232 0.058 0.239 0.013 9.059 15.10,0.0137 74.90 33.51 14.98 0.367 0.058 0.372 0.074 2.235 14.98,0.0748 83.70 44.04 15.13 0.040 0.058 0.070 0.018 1.901 15.13,0.0189 61.90 9.29 15.13 0.420 0.058 0.024 0.002 6.663 15.13,0.002

7. 实验结论

在物屏像屏距离D(D,4f)时，待测凸透镜由实验所测数据分析结果比较:

表11

物屏像屏距离D和两次透凸透镜的焦距(cm) 物屏像屏距离DD值序号 f',f',u 镜距离d的比值 D(cm) ,，，fd

1.901 D83.70 15.13,0.018 8

15.14,0.014D 77.75 2.123 1

D 74.90 2.235 14.98,0.074 7

D 72.95 2.416 15.11,0.012 4

15.14,0.010D 67.95 3.032 2

D 63.05 5.105 15.18,0.006 3

15.13,0.002D 61.90 6.663 9

D 61.15 9.059 15.10,0.013 6

D 59.90 16.06 14.91,0.010 5

l, should be removed or fixed, demolition work in a restricted area, under supervisedateriallowed to throw up or down the materials and tools and other objects. 10, the construction site, where a fall may be of any ml not be any chaos on the walkway placed or dropped down, keep working the aisles clear. 9, when working at height, are not ad shallition work is high, disassembly of the materials, construction waste should be cleaned up and removed in a timely manner, anight, all items should be stacked smooth, can not be placed in or near the hole, and not interfere with traffic. 8, when demoblocks, railings or other safety devices. 7, when working at he-on the circumstances provided channel. 6, vacant jobs, should have a firm foothold and properly tie off belts field should be configured depending-the balcony, climbing and walking in the non nstruction workers should be provided for channel up and down, do not climb scaffolding, acrossheld equipment should be checked before use to ensure safe and secure. Edges of opening job preventing objects falling. 5, co-e correct. 4, various types of handmust bas not to slip in danger of falling. 3, in the climbing operations, structure must be solid and reliable climbing equipment, s, high heels, tools should turn into a tool bag. 2, high operating personnel is strictly prohibited to fight each other, so sliding shoe-from a height, object hit ten basic safety requirements 1, working at height must be neat, do not wear plastic bottom action and, when traction on ramps, a car and you were allowed to jobs and remain at the bottom. Ten, the prevention of fallseen trd not back down. 10, motor vehicles towing vehicle with no brakes, traction object objects shall not, shall not enter is betwock to obstruct traffic; avoid vehicle, should not avoid two

car intersection, not dead standing next to the parking lot couland uneven rows of flshaped pieces of wood on either side of the wheel. 9, the presence of motor vehicles should avoid walking on the right side, -t. 8, when loading and unloading operation, if the vehicles parked on the ramp, it should be fixed with wedget nighrricades shall be set in the road safety labels, safety signs and protective measures, and to ensure that adequate lighting adestrians crowded locations and access door. 7, and scaffolding near the motorway operation area and other facilities, and babridges, forks road, slow pe speed\namely: road conditions unknown to slow, bad line slowly, slower start, passing, parking, narrow roads, detours, road-row space should be free of command. 6, the site traffic comes into play to slow down and do it \"fournar avoid vehicles falls when you start braking. 5, and from the construction site, pitch turning, reversing, when driving in the unstable objects falling hurts. 4, take the vehicle in a safe place, head, hands and body shall not reveal the compartment to high and ultra wide strapping should be solid and reliable, should prevent the car-ultra 6

voltage 1000 v following 1-15 kV 20-40 kV 60-110 kV 220,000 v Allow minimum distances with the transmission line (m) vertical 1.5 level 1 1.5 2 3 4 5 6 4 6 18th: lamp voltage may not exceed 36 volts, when working in a damp place or metal containers, lamp voltage may not exceed 12 volts. 19th: pressure vessel should have a safety valve, pressure gauge, and avoid sun exposure, collisions, oxygen cylinders to prevent contaminated oil; of acetylene gas, LPG, must have a safety device to prevent tempering. 20th: x-ray and gamma-ray flaw detector operation area, non-operator, not allowed to enter. Article 21st: corrosion, dust and radioactive and toxic work, protective measures are required, and to carry out regular inspection. Spider-man 22nd section III: Spider-man to regular medical examinations of the medical diagnosis, who suffer from high blood pressure, heart disease, anemia, epilepsy and other discomfort in the Spider-man shall not engage in aerial work. 23rd: Spider-man dressed spirit, banned the wearing of hard bottom and easy slip-on shoe nail. 24th: Spider-man material stack stationary, tools should turn into a tool bag, transfer prohibited throwing of objects. 25th: in case of bad weather (such as wind in the above grade) construction safety, prohibition of the open air, lifting and piling. 26th article: ladder shall not deficiency document, no padded using, ladder cross document spacing to 30 cm suitable, using Shi top to tied prison, bottom should take anti-sliding measures, single ladder and ground angle to 60 degrees suitable, ban II people while in ladder Shang job, as needed received long using, should lashing firm, people Word ladder in end of feet pulled prison, in channel at using ladder, due guardianship or set fence. 27th: no security measures, prohibited in hip joints,

supports, trusses of the roof truss cantilever beams, and choose the frame and half fixed widget or job to walk on, Spider-man and the ground ... Nine, ten basic security to prevent vehicle damage claim 1, without legal training of qualified certified personnel not familiar with vehicle performance is not driving a car. 2, should insist on doing defense work, vehicle brake, Horn, steering systems, lighting and other safety components such as poor are not allowed out of the car. 3, dump truck, dump truck car hop is strictly prohibited, prohibited goods mixing, loading of vehicles should not overload,

由两次成像法所测得凸透镜焦距的实验结果即测量值及其标准不确定f'f'

15.13,0.002度的变化规律是“物屏像屏距离D= 61.90 cm，=()cm”f',f',u9,，，f

f'时的标准不确定度最小。由表11看出，当D>61.90cm或D<61.90cm时，不确定度都大于0.002cm。因此，可以认为:当物屏像屏距离D= 61.90 cm时，实验9

15.13,0.002结果=()cm最接近凸透镜焦距的真实值，即在测焦距时D值的f'

选取并非越是大于4越好。这是我们在实验中发现为什么在同一台仪器上不同f'

的实验者用相同的测量方法测同一凸透镜焦距，测量结果相差很大的原因之一。

同时，在本实验测量时物屏像屏间距离D和两次成像时凸透镜位置的距离f'

d的比值结果还可以得出这样的结论:物屏像屏间距离D与两次成像时凸透镜位置的距离d之比值随着物屏像屏间距离D的减小而增大，而此值在约6.7倍时不确定度最小。

通过本次实验得出的结论，本人认为实验教学的内容还有待扩展，如何加强开放性实验或设计性实验的教学环节，让学生自主的去探究实验中出现的问题，如为什么测量误差较大，误差产生的原因及怎样找到解决的办法等等，而不是只在规定的学时内做完老师规定的实验项目就算合格。这种探究式的学习将会促使

并从中真正的学生去主动思考实验中的问题，培养和提高解决实际问题的能力，感悟到物理实验的乐趣，以使实验内容更加充实和生动。

注释

[1] 李晓彤,岑兆丰. 几何光学相差.光学设计[M].杭州:浙江大学出版社，2003版，47 [2] 杨述武. 普通物理实验(力学及热学部分)[M]. 北京:高等教育出版社,2000年版，11 [3] 杨述武,王定兴. 普通物理实验(三、光学部)[M].北京:高等教育出版社，2000年版，

40-41

[4] 杨述武,王定兴. 普通物理实验(三、光学部)[M].北京:高等教育出版社，2000年版，

参考文献

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[2] 杨述武,王定兴. 普通物理实验(三、光学部)[M].北京:高等教育出版社，2000年版，

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[3] 杨之昌.几何光学实验 [M].上海:上海科技出版社， 1984年版，75-80 [4] 沈元华,陆申之. 基础物理实验[M].北京:高等教育出版社，2003年版,226-230 [5] 辛旭平,周芹. 一级物理实验[M].北京:科学出版社，2005年版,3-15 [6] 胡根大,洪鹏程. 物理实验教程[M].上海:上海大学出版社，2006年版,3-16 [7] G.Brooker Modern Classical Optics(现代经典光学)[M].北京:科学出版社，2009年

版,8-9

security to prevent vehicle damage claim 1, without legal training of qualified c-n, Spiderhip joints, supports, trusses of the roof truss cantilever beams, and choose the frame and half fixed widget or job to walk o ed inin end of feet pulled prison, in channel at using ladder, due guardianship or set fence. 27th: no security measures, prohibit ees suitable, ban II people while in ladder Shang job, as needed received long using, should lashing firm, people Word laddersliding measures, single ladder and ground angle to 60 degr-o 30 cm suitable, using Shi top to tied prison, bottom should take antiair, lifting and piling. 26th article: ladder shall not deficiency document, no padded using, ladder cross document spacing tad weather (such as wind in the above grade) construction safety, prohibition of the open man material stack stationary, tools should turn into a tool bag, transfer prohibited throwing of objects. 25th: in case of b-on shoe nail. 24th: Spider-and easy slipman dressed spirit, banned the wearing of hard bottom -man shall not engage in aerial work. 23rd: Spider-discomfort in the Spider medical examinations of the medical diagnosis, who suffer from high blood pressure, heart disease, anemia, epilepsy and other man to regular-man 22nd section III: Spider-d, and to carry out regular inspection. Spideroperator, not allowed to enter. Article 21st: corrosion, dust and radioactive and toxic work, protective measures are require-ray flaw detector operation area, non-maray and gam-cylinders to prevent contaminated oil; of acetylene gas, LPG, must have a safety device to prevent tempering. 20th: x exceed 12 volts. 19th: pressure vessel should have a safety valve, pressure gauge, and avoid sun exposure, collisions, oxygen tage may not exceed 36 volts, when working in a damp place or metal

containers, lamp voltage may not110 kV 220,000 v Allow minimum distances with the transmission line (m) vertical 1.5 level 1 1.5 2 3 4 5 6 4 6 18th: lamp vol-40 kV 60-15 kV 20-following 1 1000 vs, and overhead transmission line of recently distance should not is less than Xia table provides: transmission line voltage d will lifting arm falls, in overhead line side work Shi, regardless of in any situation Xia, lifting arm, and rope or weightshoul olation protection measures, crane shall not in overhead transmission line following work, through overhead transmission lineanical stroke range. 17th article: in overhead transmission line following work should blackout, cannot blackout Shi, due isto clean and repair, it is strictly forbidden to head reaches into the mech 7

[8] 易明. 现代几何光学[M].南京:南京大学出版社，1986年版,27-32

[9] 百庭柱,金伟其. 光电成像原理与技术[M]. 北京:北京理工大学出版社,2006年

版,30-39

[10]杨述武. 普通物理实验(力学及热学部分)[M]. 北京:高等教育出版社,2000年版，11-12

should have a firm foothold and properly tie off belts field should be configured depending-the balcony, climbing and walking in the non nstruction workers should be provided for channel up and down, do not climb scaffolding, acrossheld equipment should be checked before use to ensure safe and secure. Edges of opening job preventing objects falling. 5, co--e correct. 4, various types of handmust bas not to slip in danger of falling. 3, in the climbing operations, structure must be solid and reliable climbing equipment, s, high heels, tools should turn into a tool bag. 2, high operating personnel is strictly prohibited to fight each other, so sliding shoe-from a height, object hit ten basic safety requirements 1, working at height must be neat, do not wear plastic bottom action and, when traction on ramps, a car and you were allowed to jobs and remain at the bottom. Ten, the prevention of fallseen trultrad not back down. 10, motor vehicles towing vehicle with no brakes, traction object objects shall not, shall not enter is betwock to obstruct traffic; avoid vehicle, should not avoid two car intersection, not dead standing next to the parking lot couland uneven rows of flshaped pieces of wood on either side of the wheel. 9, the presence of motor vehicles should avoid walking on the right side, -t. 8, when loading and unloading operation, if the vehicles parked on the ramp, it should be fixed with wedget nighrricades shall be set in the road safety labels, safety signs and protective measures, and to ensure that adequate lighting adestrians crowded locations and access door. 7, and scaffolding near the motorway operation area and other facilities, and babridges, forks road, slow pe speed\namely: road conditions unknown to slow, bad line slowly, slower start, passing, parking, narrow roads,

detours, road-row space should be free of command. 6, the site traffic comes into play to slow down and do it \"fournar avoid vehicles falls when you start braking. 5, and from the construction site, pitch turning, reversing, when driving in the unstable objects falling hurts. 4, take the vehicle in a safe place, head, hands and body shall not reveal the compartment to 8

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