五、实验数据处理计算每个圆环的半径Matlab计算程序:程序一:计算圆环半径并绘制圆环图像clc,clearl=[27.09427.01226.94326.85926.78026.70126.61526.52326.43426.332...26.23426.13826.03025.91925.79925.66925.54025.38525.20925.018...22.31922.15421.98121.82221.69121.58821.44421.33021.22221.105...21.01420.91520.82120.74020.65520.56120.48020.41520.33920.251];R=[];Ri=[];theta=0:0.001:2*pi;fori=1:20;D=l(i)-l(41-i);R=D/2;Ri=[Ri;R]figure(1)x=R*sin(theta);y=R*cos(theta);plot(x,y,'-r')axisequalholdonendRi计算结果:牛顿环2.计算透镜的曲率半径程序二:计算透镜的曲率半径clc,clearl=[27.09427.01226.94326.85926.78026.70126.61526.52326.43426.332...26.23426.13826.03025.91925.79925.66925.54025.38525.20925.018...22.31922.15421.98121.82221.69121.58821.44421.33021.22221.105...21.01420.91520.82120.74020.65520.56120.48020.41520.33920.251];R=[];theta=0:0.001:2*pi;Ri=[];fori=1:20;D=l(i)-l(41-i);R=D/2;Ri=[Ri;R];endr=[];forj=1:15ri=(Ri(j).^2-Ri(5+j).^2)./(5*589*10^(-6));r=[r;ri];endrg=mean(r)t=1:20;plot(t,Ri.^2)计算结果:rg=879.9384(mm)Rm^2-m图像由上图可知,其斜率的绝对值应为,实验所用的钠光波长为:589nm,带入计算得:,与公式法计算所得结果基本吻合!Matlab计算程序:程序二:计算不确定度clc,clearl=[27.09427.01226.94326.85926.78026.70126.61526.52326.43426.332...26.23426.13826.03025.91925.79925.66925.54025.38525.20925.018...22.31922.15421.98121.82221.69121.58821.44421.33021.22221.105...21.01420.91520.82120.74020.65520.56120.48020.41520.33920.251];R=[];theta=0:0.001:2*pi;Ri=[];fori=1:20;D=l(i)-l(41-i);R=D/2;Ri=[Ri;R];endr=[];forj=1:15ri=(Ri(j).^2-Ri(5+j).^2)./(5*589*10^(-6));r=[r;ri];endrg=mean(r)bar_r=mean(r);u_r=std(r)/sqrt(length(r));delta=0.001/sqrt(3);cu_r=rg*sqrt((u_r/bar_r)^2+delta^2)计算结果:rg=879.9384(mm)cu_r=3.8443(mm)六、实验结论及误差
分析
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1.实验结论在误差允许范围内,实验所用透镜的曲率半径为:2.误差分析透镜接触点容易产生形变引起光程差的误差。在移侧显微镜读数时,由于光线问题,容易引起对准误差、读数误差。