Optimization design and test of a high-precision measuring device of liquid refractive index based on the method of minimum deviation angle

名称	型号	厂商
高精度手动折射率测量仪	SpectroMaster®	TRIOPTICS
高精度台式液体折射仪	Abbemat 550	奥地利安东帕公司
手持式参考测温仪	1524	美国福禄克公司
空心三棱镜	/	苏州诺威特测控科技有限公司
数字气压表	370	美国Setra公司
温湿度计	608-H1	德图仪表（深圳）有限公司
恒温水浴	RTS-0AT	湖州唯立仪表厂

Table 2. Experimental reagent
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Table 2. Experimental reagent
名称级别或标准号生产厂家
纯水电阻值大于18 MΩ 自制
异辛烷纯度99.8% 阿拉丁
四氯乙烯纯度≥99% 阿拉丁

Table 3. Experimental data and statistical analysis of liquid refractive index

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Table 3. Experimental data and statistical analysis of liquid refractive index

待测液体	目标温度（ °C）	1	2	3	4	5	6	平均值 $ \overline {{n_x}} $	标准偏差S
水	15.00	1.3333632	1.3333648	1.3333695	1.3333654	1.3333665	1.3333647	1.3333657	2.16×10−6
	20.00	1.3329905	1.3329922	1.3329929	1.3329924	1.3329916	1.3329918	1.3329919	8.25×10−7
	25.00	1.3325078	1.3325084	1.3325059	1.3325063	1.3325068	1.3325080	1.3325072	1.01×10−6
异辛烷	15.00	1.3939165	1.3939148	1.3939190	1.3939154	1.3939136	1.3939173	1.3939161	1.92×10−6
	20.00	1.3914694	1.3914681	1.3914691	1.3914691	1.3914695	1.3914681	1.3914689	6.27×10−7
	25.00	1.3890532	1.3890495	1.3890541	1.3890508	1.3890477	1.3890510	1.3890511	2.35×10−6
四氯乙烯	15.00	1.5084995	1.5085050	1.5085023	1.5084986	1.5084993	1.5085052	1.5085017	2.96×10−6
	20.00	1.5057895	1.5057887	1.5057908	1.5057941	1.5057903	1.5057909	1.5057907	1.86×10−6
	25.00	1.5031255	1.5031256	1.5031264	1.5031251	1.5031268	1.5031262	1.5031259	6.38×10−7

Table 4. Comparative results of two different principles

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Table 4. Comparative results of two different principles

待测液体	最小偏向角法测量平均值	全反射角法测量平均值	折射率测量偏差
水	1.3329919	1.332993	−1.1×10⁻⁶
异辛烷	1.3914689	1.391467	1.9×10⁻⁶
四氯乙烯	1.5057907	1.505790	7.0×10⁻⁷

Table 5. Refractive indices of liquid at ambient temperature

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Table 5. Refractive indices of liquid at ambient temperature

测温( °C)	18.97	19.75	19.92	19.99	20.02
水	1.3330691	1.3330121	1.3329953	1.3329932	1.3329896
(20±1) °C时，水折射率随温度变化系数：−7.6×10⁻⁵/°C
测温(°C)	20.04	20.14	20.32	20.40	20.77
异辛烷	1.3914895	1.3913984	1.3913075	1.3912616	1.3910314
(20±1) °C时，异辛烷折射率随温度变化系数：−6.1×10⁻⁴/ °C
测温(°C)	19.20	19.31	19.90	19.98	20.08
四氯乙烯	1.5062404	1.5062193	1.5058509	1.5058002	1.5057544
(20±1) °C时，四氯乙烯折射率随温度变化系数：−5.8×10⁻⁴/°C

Table 6. Standard uncertainty introduced by air refractive index
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Table 6. Standard uncertainty introduced by air refractive index
待测液体 $ u({n_0}) $ $ {n_x} $ u₁
水 3.46×10−6 1.3329932 4.62×10−6
异辛烷 3.46×10−6 1.3914727 4.82×10−6
四氯乙烯 3.46×10−6 1.5058002 5.22×10−6

Table 7. Standard uncertainty introduced by temperature measurement error

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Table 7. Standard uncertainty introduced by temperature measurement error

待测液体	a	b	$ {c_t} $	$ {u_2} $
水	−8.11×10−5	−3.63×10−6	−8.11×10−5	−1.40×10−6
异辛烷	−4.84×10−4	−4.72×10−6	−4.84×10−4	−8.39×10−6
四氯乙烯	−5.48×10−4	1.25×10−4	−5.48×10−4	−9.49×10−6

Table 8. Experimental data of vertex angle and minimum deviation angle
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Table 8. Experimental data of vertex angle and minimum deviation angle
待测液体顶角A 最小偏向角D $ {n_x} $
水 54.99965° 20.97748° 1.3329932
异辛烷 54.99972° 24.95978° 1.3914727
四氯乙烯 54.99970° 33.10221° 1.5058002

Table 9. Standard uncertainty introduced by angle measurement error

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Table 9. Standard uncertainty introduced by angle measurement error

待测液体	$ {u_{{\rm{rad}}}} $	$\dfrac{ {\partial {n_x} } }{ {\partial A} }$	$\dfrac{ {\partial {n_x} } }{ {\partial D} }$	$ {u_3} $
水	1.41×10−6	4.27	1.71	6.46×10−6
异辛烷	1.41×10−6	4.33	1.66	6.52×10−6
四氯乙烯	1.41×10−6	4.45	1.56	6.63×10−6

Table 10. Uncertainty component and combined uncertainty

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Table 10. Uncertainty component and combined uncertainty

待测液体	$ u_s^{} $	$ {u_1} $	$ {u_2} $	$ {u_3} $	$ u({n_x}) $
水	3.37×10−7	4.62×10−6	−1.40×10−6	6.46×10−6	8.1×10−6
异辛烷	2.56×10−7	4.82×10−6	−8.39×10−6	6.52×10−6	1.2×10−5
四氯乙烯	7.59×10−7	5.22×10−6	−9.48×10−6	6.63×10−6	1.3×10−5

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Xing-li FU, Jie FENG, Xiao-hui FAN, Meng-yun PAN, Qiu-ye WEI. Optimization design and test of a high-precision measuring device of liquid refractive index based on the method of minimum deviation angle[J]. Chinese Optics, 2022, 15(4): 789

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Paper Information

Category: Original Article

Received: Apr. 8, 2022

Accepted: --

Published Online: Sep. 6, 2022

The Author Email:

DOI:10.37188/CO.2022-0064

Topics

Table 1. Experimental instruments

Table 1. Experimental instruments

Table 2. Experimental reagent

Table 2. Experimental reagent

Table 3. Experimental data and statistical analysis of liquid refractive index

Table 3. Experimental data and statistical analysis of liquid refractive index

Table 4. Comparative results of two different principles

Table 4. Comparative results of two different principles

Table 5. Refractive indices of liquid at ambient temperature

Table 5. Refractive indices of liquid at ambient temperature

Table 6. Standard uncertainty introduced by air refractive index

Table 6. Standard uncertainty introduced by air refractive index

Table 7. Standard uncertainty introduced by temperature measurement error

Table 7. Standard uncertainty introduced by temperature measurement error

Table 8. Experimental data of vertex angle and minimum deviation angle

Table 8. Experimental data of vertex angle and minimum deviation angle

Table 9. Standard uncertainty introduced by angle measurement error

Table 9. Standard uncertainty introduced by angle measurement error

Table 10. Uncertainty component and combined uncertainty

Table 10. Uncertainty component and combined uncertainty