AN INTRODUCTION TO LAB COURSES IN PHYSICS

 

V K Vaidyan

Department of Physics, University of Kerala, Trivandrum –695 581

 

 

INTRODUCTION

In general, laboratory courses in physics are designed to achieve the following objectives:

Ø      To familiarise students with some modern scientific instruments.

Ø      To illustrate topics covered the lecture courses and in some cases to extend the subject matter of the lecture courses.

 

PREPARATION OF REPORTS

There is no method of reporting, which is universally accepted or applicable to all experiments. However, the following points should be used as a guide:

 

• Students should keep a notebook in which he records his experimental results as he takes them, and any calculations done with them. These notes must be clear rather than particularly neat, as the student is required to submit a report on the experiment he had performed a few weeks later.

 

• Generally the report starts with an Introduction. This should explain the object of the experiment and the extent to which it is related to other topics in physics. Further, it should show the student understands why he did the experiment.

 

• A description of the apparatus used is best given in diagrammatic form and the text should be kept short. The limitations of the apparatus in range or accuracy should be pointed out. Also indicate the precautions taken to minimise errors and suggest how the apparatus could have been improved. This section should also include how the experiment was performed.

 

• A section must obviously be devoted to the results. It is always desirable to give some of the raw data, but many of the results can be given in the processed form (say, as graphs). It is often appropriate to indicate the weight, which can be attached to a particular reading and to indicate probable errors in graphical points with error bars. Adopt sensible scales for graphs, label axes and state units.  Draw smooth curves to give the best fit to the data, recognizing the probable error in each point.

 

• The report must close with a discussion of results obtained and conclusions drawn there from. The results should include an estimation of experimental errors and significance of the data. A discussion of the discrepancy between the experimental and the standard/ theoretical value(s) in light of the estimated error should be included.

 

MEASUREMENT AND ERROR

All measurements are subject to error, and it is important to know the effect of these errors on the final result. Hence, it is necessary to consider the sources of error both in the designing and in carrying out any experiment.

 

A single measurement can be made only to a certain accuracy, which depends on the minimum scale division of the scale being used, and the degree of definition of the indicated point. These depend on the apparatus, which must be sufficiently refined for the task. In addition, there are ultimate natural limits to the precision of a single observation, for example by the diffraction of light, by thermal vibrations of the apparatus, and even by the quantum nature of matter.

 

When one reading or a series of readings is taken, the limit to which we are working should be noted. For example, a length
(l cm) measured with a metre scale may be given as l ± 0.5 cm. An error estimated in this way should usually be the limiting error.

 

In addition to the limited precision of which we are conscious in taking readings, other kinds of error, which are likely to be present in experiments, are (i) careless errors, (ii) systematic errors and (iii) random errors.

 

Careless errors are due to definite mistakes (e.g., in reading scales, in counting oscillations, in writing down the values) or due to careless settings of cross-wires, etc. They will become obvious when the setting, reading and recording are repeated. Every measurement, however simple, should therefore be done at least twice.

 

Systematic errors are characteristic of the apparatus (or of bias consistently caused by either the surroundings or the observer). They will affect every reading in the same dire4ction and cannot be corrected by averaging a number of readings. They must therefore be recognised in advance by a careful survey. If they cannot be avoided by readjustment, they should either be eliminated by some cancellation process, or corrected after determination by some subsidiary experiment. Systematic errors will arise from incorrect zero adjustment, error of scale calibration, the use of incorrect values for constants, etc.

 

Random errors are those, which give a spread of answers on repetition. These are due to fluctuations in conditions, to unavoidable variations in the instrument, or subjective variations in the setting of or reading as determined by the observer. Such errors are always present, although careful design will often greatly reduce them. The remaining, if significant, must be treated statistically.

 

GRAPHICAL REPRESENTATION OF RESULTS

Graphical representation is an excellent way of presenting results in a compact form. It is also one of the best methods of detecting and eliminating experimental errors. Wherever possible, the data should be used in such a way that the resulting graph is a straight line. If we are confident on theoretical experimental grounds that the graph should pass through the origin, this can be extremely helpful in drawing the best straight line through the available data, as we know definitely that at least one point with zero inaccuracy. The relations that can be used or modified to draw straight-line graphs are given in Table 1.

 

Table 1. Relations and their linear forms

Relation	Linear form	Coordinantes
y = Ax + C	y = Ax + C	y, x
y = Axn	log y = log x + log A	log y, log x
y = A(x + x0)n	y1/n = A1/nx + A1/nx0	y1/n, x
y = Ax2 + Cx	y/x = Ax + C	y/x, x
y = y0 exp(-x/x0)	ln y – ln y0 = -x/x0	log y, x

 

All graphs should have clearly labelled axes and should have a caption. It is customary to plot the independent variable on the x-axis and the dependent variable on the y-axis. Thus, for a frequency response curve, frequency (f) [often log f] is plotted on the x-axis, and amplitude on the y-axis.