Experimental physics

The refractive index of water

Introduction

In this investigation, you will be observing the apparent positions coins underwater in order to measure the refractive index of water. After this, you will be observing the refraction of light in water. The investigation is designed to give you an understanding of:

Snell's law

Ray tracing to explain observations

Theory

The following information may be useful.

Figure 1 - Ray angles at a refraction boundary are measured with respect to a 'normal'.

What you will need

Assemble this equipment before you start the exercise:

A tall transparent container (20 cm or higher). Note: a square or rectangular container such as the one shown on the right works better for part 2.

A ruler

A long, straight object that can withstand getting wet, such as a pen, a skewer or a straw.

Two identical coils (for example, two 10c coins).

Not necessary, but may be helpful:

Sticky tape (to stick on the side to mark different heights)

A jug (to pour the water)

A permanent marker (to mark heights on the sticky tape)

Part 1-Measuring nwater

Procedure

1. Choose five (5) evenly spaced heights on your container (do not start at zero). You may want to mark these heights on the side of the container. If you stick sticky tape on the side of the container first, then it will not be permanently marked.

2. Fill the container to the lowest of these heights and record this in the results table.

3. Place one coin on the bottom of the container (it is underwater). Look at the container from above and move the other coin beside the container (it is in air) until the two coins looks like they are at the same height (note: they will not be at the same height, but they will look like they are, because they will appear to be the same size to you).

Figure 2 - Comparing the apparent positions of two coins, one submerged underwater.

4. Record the height of the coin in air relative to the surface of the water (labelled heoin in figure). Try to estimate the uncertainty in this height by working out the range of heights over which they look like they are at the same height. As this is a matter of judgement, you may have relatively large uncertainties, and this is okay. You may be able to reduce these uncertainties by taking a photo and working out when the two coins are the same size.

Include a discussion of how you calculated these uncertainties in your report.

5. Now add water to the container until the water level is at the next height. Repeat steps 3 and 4, obtaining the distance between the outside coin and the water surface when the coins look like they are at the same height. Record your measurements in the results table.

6. Repeat these steps for the three remaining heights.

Results

Record your results in a table like this one.

Estimate the uncertainty in hwater from how precisely you think you have measured the height of the water in the container.

Analysis

Plot a graph with hwater on the Y-axis and hcoin on the X-axis. The gradient of the graph should be the refractive index of water.

You may wish to use the Excel template Linear plot with uncertainties.xis to plot this graph (it is available onll the Moodle page), and note the equations of the line of best fit, and the two lines of worst fit.

Record your value for nwater with an uncertainty.

Include a discussion of how the uncertainties were calculated.

Include a screenshot of this graph in your report.

Part 2-Observing refraction

Procedure

1. Place your straight object (the pen/skewer/straw, etc) so that is it half submerged under the water.

2. Gradually change the angle that the straight object makes with the surface of the water as shown in the diagram.

3. Photograph your object as it makes different angles with the water (say, three photos). Include a label in the frame. of each of your photographs that contains your name, zlD and the date.

4. Describe how your observations change as the angle changes.

Figure 3-This diagram shows how the straight object actually is, but you will observe where it appears to be.

Figure 4-This photo shows a good angle to take your photographs. The long straight object has been omitted.

Questions

1. Explain, using equations and diagrams, why the gradient of the graph you plotted in part 1 is equal to the refractive index of water, nwater. For this equation, do the derivation algebraically; do not refer to the value that you have measured.

2. Compare the value that you have measured for nwater to the accepted value of nwater = 1.33. Discuss any discrepancies; make sure that you refer to the size of your uncertainty in your answer.

3. Suggest a better technique to measure nwater. This technique does not have to be limited by the equipment you have at home -you may propose any equipment that you think is necessary.

4. Use ray tracing to clearly explain why the straight object looks the way it appears to you in the water. This answer requires diagrams and words (and possibly equations). Marks will be awarded for clarity. Hint: Consider light reflected of the far, submerged end of the straight object. How does it get to your eye?