Law of refraction
Using a semicircular block to investigate refraction.
Apparatus and materials
For each student or group of students
Semicircular Perspex or glass block
Lamp, stand, housing and holder
Power supply for lamp
Card and suitable adhesive
Health & Safety and Technical notes
This activity may take some time if done carefully, so the lamps may become hot. Students should be warned of this fact.
The base of the block should be frosted or painted with white paint, or total reflection at the base will prevent the path of the ray through the block being visible.
A parallel-sided glass block will also do the job, but there will be two refractions to deal with.
a Stick card to the flat face of the semicircular block, so that only a vertical slit is exposed at the middle of the flat face.
b Place the block on the sheet of paper and direct a ray streak onto the slit. Observe the ray tracks and measure the angles. Change the angle with which the ray strikes the flat face, and record the angles of incidence and refraction again. Repeat the process as often as required.
c Values of sin i/sin r can be calculated for each pair of readings, or a graph plotted of sin iagainst sin r and the gradient measured to give the refractive index.
d Students may also direct the ray in through the curved face to observe refraction and total internal reflection.
1 To make the measurement of angles simpler and faster, the block can be placed on a protractor template.
2 Because the rays emerge from the semicircular block along a radius of the circle, there should be no deviation when they emerge from the block. Thus angles can be read directly from the protractor template, or marked on the paper to be measured later. This also shows that there is no refraction when light strikes an interface normally, even when the interface is curved.
3 Students may also direct the ray streaks in through the curved face, to observe refraction and total internal reflection.
4 If semicircular boxes of thin transparent plastic are available (such as are sometimes used for small cheeses), these can be filled with water and used for this experiment. If the experiment is done as a demonstration, a Hartl optical disc or similar device can be used to show a ray being refracted as it passes through the centre of a semicircular slab.
5 Pieces of glass are very useful for changing the direction of a ray of light, and prisms can even send it back the way it came.
6 How Science Works Extension: Before students have been introduced to Snell’s law and the significance of the sines of the angles, they can examine the results from this experiment and plot a graph of angle of refraction against angle of incidence. If they have covered only a small range of angles, this will approximate to a straight line. However, if they have covered a good range (say, 10° to 80°), they should obtain a graph which is clearly a curve. This should alert them to the fact that results don’t always fall on a simple straight line!
The tables provide two sets of data to illustrate this. Students could be provided with Table 1 and asked to plot a graph; it is almost a straight line. Table 2 has data over a wider range, showing that the relationship between i and r is not a straight line.
7 Rather than telling your students that the relationship is one of sines, you could ask them to construct right-angled triangles as shown in the diagram, and tabulate values of the opposite sides. This should give a straight line graph. Then you can move more logically to the sines of the angles.
8 Plotting a graph of sin i against sin r is a good test of the data. How good a straight line results? It is likely that angles will have been measured to the nearest degree. For a particular value of i, try values of r lying 1° either side of the measured value. Where do these points lie on the graph? This will help to give students an idea of the precision of their measurements, and a sense of the uncertainty in the graph line.
The gradient of the graph is the refractive index n. If you have blocks of different materials, compare these. Since their refractive indexes are likely to be similar, the results will be similar. This should emphasize the need for precise measurements if this method is to be used to determine values of n. A spectrometer allows more precise measurements (to a fraction of a degree). Other methods of determining n include immersion of a material in liquids of known refractive index.
9 In English-speaking countries, the law of refraction is known as Snell’s law, after the Dutch mathematician Willebrord Snellius; in France, it is known as Descartes’ law. Both contributed to our understanding of refraction. However, the earliest record of the law is in a manuscript by Ibn Sahl, dated 984, six centuries before either of the Europeans did their work.