Introduce the student to the laboratory activities of geometrical optics and provide the basic principles of the statistical analysis of experimental data. Students must achieve a good degree of autonomy in the laboratory to the measure of optical quantities and in the processing and analysis of experimental data with the aid of computer tools.
teacher profile teaching materials
Tools and measures. Measurement units - Trigonometry angles and definitions - Sizes and errors - Systematic error and random error - Instrument error - Standard deviation and standard error - Error propagation - Representing data: significant figures, comparison of measurements, tables and graphs, histograms
Descriptive statistics. Indices of central tendency: average, median and mode - Percentiles - Indices of variability: variance and standard deviation - Limit distributions
Correlation between variables. Linear regression, least squares method - Linearization of a function - Verification of the acceptability of a fit: Chi square test and determination coefficient - Pearson r coefficient, Spearman correlation coefficient for ranks
Probability. Definition and fundamental properties - Probability distributions (binomial, Poisson and uniform distribution - Gaussian and error integral, justification of sum in quadrature and standard deviation of the mean, standard normal distribution) - Average and variance of a random variable - Confidence intervals - Standard deviation as acceptability percentage - Applications and verifications: correlation index and chi-square test - Student's t test for comparison between measurements
Inferential statistics. Hypothesis test and significance - The null hypothesis and the alternative hypothesis - Types of studies and sampling - Sample distributions - Criterion of significance and critical values - Errors and decisions of a statistical test - Sign test - Chi square test as test of significance - z-test and t-test - Distribution F - Analysis of variance (ANOVA) with one and two ways
The topics of the laboratory exercises will be chosen from the following list
1) Use of precision instruments (decimal and twentieth caliber, spherometer) for the measurement of quantities. Statistical treatment of the error.
2) Verification of the law of light reflection from a plane mirror.
3) Verification of the law of refraction in a plexiglass plate.
4) Verification of Kepler's law on the reduction of light intensity as a function of distance.
5) Verification of the Lambert-Beer law on the attenuation of luminous intensity on passing through an opaque medium.
6) Determination of the focal distance and dioptric power of a thin lens through an optical measurement.
7) Determination of the focal distance and dioptric power of a lens system with the Bessel method.
8) Determination of the focal distance and dioptric power of an ophthalmic lens by measuring with a spherometer and with a dioptrometer and characterization of an astigmatic lens
9) Verification of Gullstrand's law and search for the main planes of an optical system consisting of two thin lenses.
10) Dispersion of light through a prism: verification of Cauchy's law and determination of the number of Abbe
11) Estimate of the magnification of an optical system: the magnifying lens
12) Use of Student's t test to compare experimental data and the chi-square test to assess how well a theoretical trend reproduces the behavior of experimental data; construction of a histogram and its limit function.
- S. Walker, Fondamenti di Fisica (Pearson, 2010)
- R. Meyer-Arendt, Introduction to classical and modern optics (Prentice Hall, 1995)
- R. Taylor, Introduzione all’analisi dell’errore (Zanichelli, 2010)
- M. Bland, Statistica medica (Maggioli Editore, 2014)
- M. M. Triola e M. F. Triola, Fondamenti di Statistica (Pearson, 2013)
- J. Welkowitz, B. Cohen e R. Ewen, Statistica per le scienze del comportamento (Apogeo)
Programme
The theoretical lessons will focus on the following topics:Tools and measures. Measurement units - Trigonometry angles and definitions - Sizes and errors - Systematic error and random error - Instrument error - Standard deviation and standard error - Error propagation - Representing data: significant figures, comparison of measurements, tables and graphs, histograms
Descriptive statistics. Indices of central tendency: average, median and mode - Percentiles - Indices of variability: variance and standard deviation - Limit distributions
Correlation between variables. Linear regression, least squares method - Linearization of a function - Verification of the acceptability of a fit: Chi square test and determination coefficient - Pearson r coefficient, Spearman correlation coefficient for ranks
Probability. Definition and fundamental properties - Probability distributions (binomial, Poisson and uniform distribution - Gaussian and error integral, justification of sum in quadrature and standard deviation of the mean, standard normal distribution) - Average and variance of a random variable - Confidence intervals - Standard deviation as acceptability percentage - Applications and verifications: correlation index and chi-square test - Student's t test for comparison between measurements
Inferential statistics. Hypothesis test and significance - The null hypothesis and the alternative hypothesis - Types of studies and sampling - Sample distributions - Criterion of significance and critical values - Errors and decisions of a statistical test - Sign test - Chi square test as test of significance - z-test and t-test - Distribution F - Analysis of variance (ANOVA) with one and two ways
The topics of the laboratory exercises will be chosen from the following list
1) Use of precision instruments (decimal and twentieth caliber, spherometer) for the measurement of quantities. Statistical treatment of the error.
2) Verification of the law of light reflection from a plane mirror.
3) Verification of the law of refraction in a plexiglass plate.
4) Verification of Kepler's law on the reduction of light intensity as a function of distance.
5) Verification of the Lambert-Beer law on the attenuation of luminous intensity on passing through an opaque medium.
6) Determination of the focal distance and dioptric power of a thin lens through an optical measurement.
7) Determination of the focal distance and dioptric power of a lens system with the Bessel method.
8) Determination of the focal distance and dioptric power of an ophthalmic lens by measuring with a spherometer and with a dioptrometer and characterization of an astigmatic lens
9) Verification of Gullstrand's law and search for the main planes of an optical system consisting of two thin lenses.
10) Dispersion of light through a prism: verification of Cauchy's law and determination of the number of Abbe
11) Estimate of the magnification of an optical system: the magnifying lens
12) Use of Student's t test to compare experimental data and the chi-square test to assess how well a theoretical trend reproduces the behavior of experimental data; construction of a histogram and its limit function.
Core Documentation
- Lecture notes distributed by the teacher during the course- S. Walker, Fondamenti di Fisica (Pearson, 2010)
- R. Meyer-Arendt, Introduction to classical and modern optics (Prentice Hall, 1995)
- R. Taylor, Introduzione all’analisi dell’errore (Zanichelli, 2010)
- M. Bland, Statistica medica (Maggioli Editore, 2014)
- M. M. Triola e M. F. Triola, Fondamenti di Statistica (Pearson, 2013)
- J. Welkowitz, B. Cohen e R. Ewen, Statistica per le scienze del comportamento (Apogeo)
Type of delivery of the course
In the theoretical lessons the statistical principles of the program will be illustrated and the methods of carrying out laboratory experiments will be illustrated. Theoretical lessons will be offered also in e-learning mode using the "moodle" platform, starting from the internet page https://scienze.el.uniroma3.it/ selecting Corsi Triennali - Ottica e Optometria - Laboratorio di Ottica Geometrica During the laboratory experiences, students will be required to verify a specific law, guided by operational instructions and the support of the teachers.Type of evaluation
Students will be assessed in progress by correcting the reports required for each laboratory experience. If this ongoing evaluation proves to be negative, the students will be required, at the end of the course, to take a practical test consisting in verifying one of the laws illustrated during the course. During the oral test the student will be asked to describe one (or more) of the experiences carried out during the laboratory, including the type of analysis performed, the treatment of errors and the statistical tests used. teacher profile teaching materials
Tools and measures. Measurement units - Trigonometry angles and definitions - Sizes and errors - Systematic error and random error - Instrument error - Standard deviation and standard error - Error propagation - Representing data: significant figures, comparison of measurements, tables and graphs, histograms
Descriptive statistics. Indices of central tendency: average, median and mode - Percentiles - Indices of variability: variance and standard deviation - Limit distributions
Correlation between variables. Linear regression, least squares method - Linearization of a function - Verification of the acceptability of a fit: Chi square test and determination coefficient - Pearson r coefficient, Spearman correlation coefficient for ranks
Probability. Definition and fundamental properties - Probability distributions (binomial, Poisson and uniform distribution - Gaussian and error integral, justification of sum in quadrature and standard deviation of the mean, standard normal distribution) - Average and variance of a random variable - Confidence intervals - Standard deviation as acceptability percentage - Applications and verifications: correlation index and chi-square test - Student's t test for comparison between measurements
Inferential statistics. Hypothesis test and significance - The null hypothesis and the alternative hypothesis - Types of studies and sampling - Sample distributions - Criterion of significance and critical values - Errors and decisions of a statistical test - Sign test - Chi square test as test of significance - z-test and t-test - Distribution F - Analysis of variance (ANOVA) with one and two ways
The topics of the laboratory exercises will be chosen from the following list
1) Use of precision instruments (decimal and twentieth caliber, spherometer) for the measurement of quantities. Statistical treatment of the error.
2) Verification of the law of light reflection from a plane mirror.
3) Verification of the law of refraction in a plexiglass plate.
4) Verification of Kepler's law on the reduction of light intensity as a function of distance.
5) Verification of the Lambert-Beer law on the attenuation of luminous intensity on passing through an opaque medium.
6) Determination of the focal distance and dioptric power of a thin lens through an optical measurement.
7) Determination of the focal distance and dioptric power of a lens system with the Bessel method.
8) Determination of the focal distance and dioptric power of an ophthalmic lens by measuring with a spherometer and with a dioptrometer and characterization of an astigmatic lens
9) Verification of Gullstrand's law and search for the main planes of an optical system consisting of two thin lenses.
10) Dispersion of light through a prism: verification of Cauchy's law and determination of the number of Abbe
11) Estimate of the magnification of an optical system: the magnifying lens
12) Use of Student's t test to compare experimental data and the chi-square test to assess how well a theoretical trend reproduces the behavior of experimental data; construction of a histogram and its limit function.
- S. Walker, Fondamenti di Fisica (Pearson, 2010)
- R. Meyer-Arendt, Introduction to classical and modern optics (Prentice Hall, 1995)
- R. Taylor, Introduzione all’analisi dell’errore (Zanichelli, 2010)
- M. Bland, Statistica medica (Maggioli Editore, 2014)
- M. M. Triola e M. F. Triola, Fondamenti di Statistica (Pearson, 2013)
- J. Welkowitz, B. Cohen e R. Ewen, Statistica per le scienze del comportamento (Apogeo)
Programme
The theoretical lessons will focus on the following topics:Tools and measures. Measurement units - Trigonometry angles and definitions - Sizes and errors - Systematic error and random error - Instrument error - Standard deviation and standard error - Error propagation - Representing data: significant figures, comparison of measurements, tables and graphs, histograms
Descriptive statistics. Indices of central tendency: average, median and mode - Percentiles - Indices of variability: variance and standard deviation - Limit distributions
Correlation between variables. Linear regression, least squares method - Linearization of a function - Verification of the acceptability of a fit: Chi square test and determination coefficient - Pearson r coefficient, Spearman correlation coefficient for ranks
Probability. Definition and fundamental properties - Probability distributions (binomial, Poisson and uniform distribution - Gaussian and error integral, justification of sum in quadrature and standard deviation of the mean, standard normal distribution) - Average and variance of a random variable - Confidence intervals - Standard deviation as acceptability percentage - Applications and verifications: correlation index and chi-square test - Student's t test for comparison between measurements
Inferential statistics. Hypothesis test and significance - The null hypothesis and the alternative hypothesis - Types of studies and sampling - Sample distributions - Criterion of significance and critical values - Errors and decisions of a statistical test - Sign test - Chi square test as test of significance - z-test and t-test - Distribution F - Analysis of variance (ANOVA) with one and two ways
The topics of the laboratory exercises will be chosen from the following list
1) Use of precision instruments (decimal and twentieth caliber, spherometer) for the measurement of quantities. Statistical treatment of the error.
2) Verification of the law of light reflection from a plane mirror.
3) Verification of the law of refraction in a plexiglass plate.
4) Verification of Kepler's law on the reduction of light intensity as a function of distance.
5) Verification of the Lambert-Beer law on the attenuation of luminous intensity on passing through an opaque medium.
6) Determination of the focal distance and dioptric power of a thin lens through an optical measurement.
7) Determination of the focal distance and dioptric power of a lens system with the Bessel method.
8) Determination of the focal distance and dioptric power of an ophthalmic lens by measuring with a spherometer and with a dioptrometer and characterization of an astigmatic lens
9) Verification of Gullstrand's law and search for the main planes of an optical system consisting of two thin lenses.
10) Dispersion of light through a prism: verification of Cauchy's law and determination of the number of Abbe
11) Estimate of the magnification of an optical system: the magnifying lens
12) Use of Student's t test to compare experimental data and the chi-square test to assess how well a theoretical trend reproduces the behavior of experimental data; construction of a histogram and its limit function.
Core Documentation
Professors F. Offi and F. Fontana lecture notes- S. Walker, Fondamenti di Fisica (Pearson, 2010)
- R. Meyer-Arendt, Introduction to classical and modern optics (Prentice Hall, 1995)
- R. Taylor, Introduzione all’analisi dell’errore (Zanichelli, 2010)
- M. Bland, Statistica medica (Maggioli Editore, 2014)
- M. M. Triola e M. F. Triola, Fondamenti di Statistica (Pearson, 2013)
- J. Welkowitz, B. Cohen e R. Ewen, Statistica per le scienze del comportamento (Apogeo)
Type of delivery of the course
In the theoretical lessons the statistical principles of the program will be illustrated and the methods of carrying out laboratory experiments will be illustrated. During the laboratory experiences, students will be required to verify a specific law, guided by operational instructions and the support of the teachers.Type of evaluation
Students will be assessed in progress by correcting the reports required for each laboratory experience. If this ongoing evaluation proves to be negative, the students will be required, at the end of the course, to take a practical test consisting in verifying one of the laws illustrated during the course. During the oral test the student will be asked to describe one (or more) of the experiences carried out during the laboratory, including the type of analysis performed, the treatment of errors and the statistical tests used.