Refractive Index of Water
Aims
In this experiment you will measure the refractive index of a glass block and of pure water and
determine the uncertainty in your measurements.
Safety
 Switch the ray box off if it becomes too hot.
 Do not switch electrical equipment on or off with wet hands.
 If glass blocks are used, take care with sharp edges.
Equipment, materials and method
1 For this experiment you will require an A3 sheet of drawing paper, a sharp pencil, two glass or
perspex semicircular blocks, a ray box with a focusing lens, a protractor and a ruler, paper towels, a
small beaker of pure water and a dropper.
2 Using a sharp pencil, draw two lines at right angles to each other in the centre of the A3 paper.
Take care to draw thin and precise lines that intersect at exactly 90°. Place the glass block so that its
edge is along one of the lines and the intersection of the two lines is exactly in the middle of the flat
side. The line perpendicular to the flat side is a normal to the surface of this side of the block.
Part 1
Measurement of the refractive index of the glass block
Method
1 Direct a ray of light from the ray box so it passes through the curved side of the block without being
refracted and also through the point where the two lines intersect, as shown in figure 1.
Figure 1
2 Adjust the angle of incidence of this light ray until it is equal to the critical angle ic and the refracted
light ray is parallel to the flat side of the block.
3 Trace the critical ray from the ray box to the block.
4 Remove the block and complete the path of the refracted ray through the block.
5 Measure the critical angle ic as accurately as possible.
6 Repeat the measurement two more times. Record your measurements and their precision.
Questions
1 (a) Calculate the mean value of the critical angle ic and estimate its uncertainty.
(b) Use the formula
ng =
1
sin ic
to calculate the refractive index ng of the glass.
2 Use your estimate of the uncertainty and the mean value to calculate a maximum value and a
minimum value for the refractive index.
Part 2
Measurement of the refractive index of pure water
Method
1 Trap a thin layer of pure water between the semicircular glass block and a second glass block, as
shown in figure 2.
Figure 2
2 Direct a light ray as before, through the original semicircular glass block so that it passes through
the centre of its flat side.
3 Adjust the light ray to the critical position and measure the critical angle at the
glass–water boundary as before.
4 Repeat the measurement two more times. Record your measurements and their precision.
Questions
1 (a) Calculate the mean value of the measured angle ic′ and estimate its uncertainty.
(b) Use the formula
ng sin ic′ = nw sin 90°
to calculate the refractive index nw of pure water.
2 Use your estimate of the uncertainty and the mean value of ic′ and of ng to calculate a maximum
value and a minimum value for the refractive index of pure water.
3 Discuss how the uncertainty in the refractive index values could be reduced.
Teacher Notes
Aims

To measure the refractive index of a glass block and of pure water.

To determine the uncertainty in your measurements.
Safety
 Tell the students not to switch electrical equipment on or off with wet hands.
 Tell them to switch the ray box off if it becomes too hot.
 If glass blocks are used, take care with sharp edges.
 CLEAPSS information on ray boxes: Laboratory Handbook/CD-ROM section 12.16.
Teaching notes
4 Provide protractors that are as large as possible. Remind the students to ensure they draw the
reference lines carefully and place the block exactly in the correct position in each part of the
practical activity.
5 Check students repeat each measurement twice to obtain a mean value for the critical angle and its
uncertainty.
Answers to questions
Part 1
Measurement of the refractive index of the glass block
1 (a) They should obtain a critical angle of about 42° for glass and an uncertainty of about ± 1°.
(b) The refractive index depends on the type of glass and will probably be about 1.5.
2 Using the formula with a critical angle of 41° gives a maximum value for ng and with a critical angle
of 43°, a minimum value for ng. The uncertainty should be no more than about ± 0.02.
Part 2
Measurement of the refractive index of pure water
3 (a) The critical angle for a glass–water boundary should be about 62° with an uncertainty of about
± 1°.
(c) The refractive index of pure water is 1.33.
4 Using the given formula with the estimated uncertainties for ng and ic′ should give an uncertainty of
no more than about ± 0.04.
5 The critical angle in each case needs to be measured more precisely. To do so, either a
trigonometric method should be used or a larger protractor with a finer scale should be used. The
trigonometric method would involve using the normal and the incident ray as two sides of a rightangled triangle with the third side parallel to the flat side of the block. Repeated measurements
using this method would probably give an uncertainty less than the precision of the protractor and
therefore a more accurate value of the refractive indexes.
Practical assessment opportunities
6 PSA – Selecting and using equipment: 0–3 marks
(Following instructions and group work; organisation and safety assessed at end of course)
7 ISA preparation:
practical task – practice in measuring angles accurately and estimating uncertainties, in recording
measurements and in processing data
written task Section A and B – opportunities to discuss uncertainties and accuracy
Equipment and materials required
Each group or pair of students will require the following equipment:

an A3 sheet of drawing paper

a sharp pencil

two glass or perspex semicircular blocks

a ray box with a focusing lens

a protractor and a ruler

paper towels

a small beaker of pure water and a dropper
Safety
Provide a notice telling students not to switch electrical apparatus on or off with wet hands.
If glass blocks are used, take care with sharp edges.
CLEAPSS information on ray boxes: Laboratory Handbook/CD-ROM section 12.16.