PHYSICS LAB II
The course offers a unique approach to enhance the understanding of physical phenomena through the iteration between theoretical model development and refinement of experimental measurements. Often, the initial comparison between predictions from a basic theoretical model and the results of initial measurements reveals significant discrepancies, extending beyond the anticipated uncertainties due to data acquisition imprecision and error propagation.
Faced with such discrepancies, the common temptation is to attribute them to unidentified issues and put forward unverified hypotheses. However, it is precisely this discrepancy between the theoretical model and the experiment that serves as the gateway to understanding physical phenomena. Overcoming this challenge is neither simple nor guaranteed, but it is the core of our course.
The course begins by analyzing seemingly simple phenomena using basic theoretical models, as described in textbooks. Simplicity is essential because it allows for generalization and understanding of a wide range of situations. However, in many cases, the simple theoretical model fails to predict experimental results accurately in specific cases.
The course follows a series of key steps:
1. Initially, the approach involves collecting a large volume of data, hoping that the average will converge to the expected result. However, this strategy often proves insufficient as the discrepancy persists despite increasing data.
2. The next phase involves refining the experiment, starting from the assumption that the theoretical model is correct. This entails the patient and experimental identification of parameters that most significantly influence the results and optimizing experimental conditions to align them as closely as possible with the model's predictions.
3. At this point, attention shifts to the theoretical model itself. Students must acquire the ability to distinguish between measurement error due to instrument precision and the discrepancy between predictions and results, caused by the model's inadequacy in considering all factors involved in the experiment.
4. After modifying the model based on students' insights and simulating its behavior, a new comparison between predictions and experimental results is conducted. It is not uncommon for the agreement to still not be within the expected error limits.
5. The refinement process continues until identifying experimental conditions in which the modifications made to the model and the experiment bring the results within the expected error. This represents the ultimate goal of the course.
It is important to emphasize that the course's focus is not only on verifying a theoretical model in the laboratory but primarily on the development and optimization of such a model through experimental techniques. This approach allows theory and practice to be merged into a single action aimed at connecting the specific studied phenomenon with a broader understanding of the natural world."
1) The magnetic scale
The process of gravity fall of magnets of different shapes, sizes, weight, magnetic moment, mutual distance, etc. inside pipes made of different materials, having different diameter, thickness, and shape is experimentally analyzed in terms of flight times and of the electromotive force induced in electric circuits, in order to determine the spatial characteristics of the magnetic field produced by the magnet arrangements and the forces opposed to the motion that develop when the arrangement moves close to a conductive material. The analysis allows in particular developing a method of measuring the weight of a falling object without the help of any measuring instrument other than the mobile phone's chronometer.
2) The Earth's magnetic field.
The experiment aims at measuring the Earth's magnetic field by characterizing the re-orientation of the magnetic needle of a compass in the presence of competing magnetic fields, such as the magnetic field produced by an electric circuit of different orientation, distance, and current, and the perturbation produced by a static magnet sweeping close to the compass in order to perturb the compass needle equilibrium position. The spatial characteristics of the magnetic field produced by the circuit are analyzed for different shapes and orientation of the circuit in order to identify the measurement procedure that produces the maximum precision.
3) The grade of temporal coherence of an optical field
The visibility of the fringes produced by the interference between an optical field and a time-delayed replica thereof is analyzed by means of a Michelson interferometer for different time delays. The time-frequency power spectrum of the same optical field is also characterized by means of a scanning monochromator. The results obtained for optical light filed of different spectral bandwidth are compared, highlighting the connection existing between the grade of temporal coherence and the spectral bandwidth of an optical light filed.
4) The grade of spatial coherence of an optical field
The visibility of the interference pattern produced by diffraction of a light speckle field by means of a tunable slit is characterized as a function of the speckle size in the plane of the slit, in order to determine the degree of spatial coherence of the light field, wherein the size of the speckle is in ties turn controlled by means of a suitable spatial filter. The characterization of the power spectrum in the spatial-frequency domain by means of photographic acquisition of the far-field intensity spatial profile clarifies the connection that exists between the space spectral bandwidth and the length of spatial coherence of a light field.
5) The refractive index
The refractive index at 632 mn of the material of which an optical prism is made of is determined by two independent methods: (i) using a He-Ne laser at 632nm, by characterizing the reflection coefficient for the component of the laser light field polarized in the plane of incidence, in function of the angle of incidence, and (ii) using a plurality of discharge lamps with different spectral lines, by characterizing the angle of minimum deviation produced by the prism for the different wavelengths, and thus obtaining the value at the desired wavelength by suitable fitting of the data by the index dispersion relation. The comparison between the two methods allows to highlight the possible presence of systematic errors in the measurement procedure.