12.4
The Index of Refraction
OVERALL EXPECTATIONS
• investigate, through inquiry, the properties of light, and predict its behaviour,
particularly with respect to reflection in plane and curved mirrors and
refraction in converging lenses
• demonstrate an understanding of various characteristics and properties of
light, particularly with respect to reflection in mirrors and reflection and
refraction in lenses
SPECIFIC EXPECTATIONS
Developing Skills of Investigation and Communication
• use appropriate terminology related to light and optics
• calculate, using the indices of refraction, the velocity of light as it passes
through a variety of media, and explain the angles of refraction with reference
to the variations in velocity
Time
30–45 min
Vocabulary
• index of refraction
Other Program Resources
BLM 12.4-1 Math Connection:
Calculating the Speed of
Light in Various Media
Skills Handbook 5. Using
Mathematics in Science
Science Perspectives 10
website www.nelson.com
/scienceperspectives/10
Understanding Basic Concepts
• identify the factors, in qualitative and quantitative terms, that affect the
refraction of light as it passes from one medium to another
Related Resources
Gizmo: Refraction
KEY CONCEPTS
• Light changes direction predictably as it travels through different transparent media.
• Light bends toward the normal when it slows down in a medium with a higher index
of refraction.
Hecht, Eugene. Schaum’s
Outline of Optics.
McGraw-Hill, 1974.
Science Perspectives 10
ExamView® Test Bank
Science Perspectives 10
Teacher eSource SUITE
Upgrade
EVIDENCE OF LEARNING
Science Perspectives 10
website www.nelson.com
/scienceperspectives/10
Look for evidence that students can
• use the term index of refraction correctly.
• demonstrate how to use the equation n 5 c/v to determine the index of refraction of
a given medium or the speed of light through a given medium.
• describe factors that cause the refraction of light as it passes from one medium to
another
▼
SCIENCE BACKGROUND
Index of Refraction and the
Speed of Light
▼
• The results of activities 12.2 and 12.3
lead directly to the concept of the
index of refraction (also called the
refractive index). Students will have
noticed from these activities that as
the angle of refraction increases the
angle of incidence increases and that
the amount of this increase is different
for different media. Indeed, the
amount of refraction for similar
angles of incidence is an optical
property of the material and can be
used to distinguish different media.
If the ratio of sines was calculated in
the previous two activities, then the
class saw that the value obtained
from finding the ratio is constant
and different for different media.
NEL
55308_03_ch12_p827-874 pp3.indd 845
Chapter 12 The Refraction of Light
845
11/20/09 6:13:41 PM
In fact, the index of refraction can
be used to identify a medium. If a
substance has an index of refraction
of 1.52, for example, you can suspect
that it is some type of glass (see the
table on page 524 of the Student
Book).
• The index of refraction of a given
medium can be expressed in a variety
of ways. The first is the way students
did in the previous two lessons (if they
completed the trig calculations in the
Apply and Extend sections: the sine
of the angle of incidence divided by
the sine of the angle of refraction. A
second involves speeds: the speed of
light in a vacuum divided by its speed
through the given medium, or c/v.
Since n 5 c/v and n 5 sin /i / sin /R,
it follows that c/v 5 sin /i / sin /R
• These equations can be algebraically
rearranged in a number of useful
ways; for example: c 5 n/v or
v 5 c sin /R / sin /i
• As you read in the notes for
Section 12.2, the relationship n 5 c/v
was discovered twice before Snell hit
upon it again. However, Snell was the
first to express it in terms of sines of
angles. Ibn Sahi and Thomas Harriot
wrote about the ratios of speeds of
light, as did Rene Descartes. Descartes
published his discovery in 1637, but
it is generally accepted that he had
never read or heard of Snell’s work.
POSSIBLE MISCONCEPTIONS
Identify
Students may think that n 5 sin /i / sin /R and n 5 c/v are separate,
unrelated equations.
Clarify
Explain that the n in both equations represents the index of refraction. The
equations approach the problem in different ways, but they both provide the
same answer.
Ask What They Think Now
At the end of the lesson, ask students about the two ways of calculating the
index of refraction of a given material. (n 5 c/v; n 5 sin /i / sin /R)
TEACHING NOTES
Engage
• If trig ratios have been calculated in previous activities, then write “sin /i / sin /R”
on the board to have students recall what they learned about this ratio in the
previous section. Ask, What did you find out about this ratio in the previous
lesson? (For any given material, the ratio is always the same, and the number
varies from material to material.) What does this ratio tell you about how light
travels in a given material? (It is a measure of the speed of light through that
material.) Do you think the ratio could be used to compute the speed of light in
different media? Allow students to speculate about this final question. Tell
them that they will learn the answer to the question in the section to come.
• If trig ratios were not calculated in the previous section, tell the class that the
first measurement of the speed of light in a medium other than a vacuum
or air was made in 1862 by Jean Foucault. Ask, Why would anyone want to
know the speed of light in something other than a vacuum or air? (Light travels
through other transparent media; knowing how fast it travels in other media
is as important as knowing how fast it travels in air.) Explain that they will
learn an equation in this section that will be used to calculate the speed of
light in other media.
846
Unit E: Light and Geometric Optics
55308_03_ch12_p827-874 pp3.indd 846
NEL
11/25/09 12:32:19 AM
Explore and Explain
• Students may benefit from a brief review of scientific notation. Have students
review Skills Handbook 5.C. Scientific Notation. Go over the following
with the class.
– All numbers in scientific notation are expressed as a power of 10. Write the
following series on the board: 10 5 1 3 101 5 1 3 10, 100 5 1 3 102 5
1 3 10 3 10, 1000 5 1 3 103 5 1 3 10 3 10 3 10, and so on. To make
sure students understand, ask, What is 10 000 in scientific notation? (1 3 104)
– Show how to express ordinary numbers in scientific notation by writing
examples on the board: 30 5 3.0 3 101, 56 5 5.6 3 101, 279 5 2.79 3
102, 46 800 5 4.68 3 104, and so on. To test for understanding, ask, What
is 6720 in scientific notation? (6.72 3 103)
– Show how to go from scientific notation to standard notation: 7.0 3
101 5 7 3 10 5 70, 3.8 3 104 5 3.8 3 10 000 5 38 000. To test for
understanding, ask, What is 8.71 3 103 in standard notation? (8710)
– Demonstrate how to multiply and divide in scientific notation. Multiply
and divide the standard decimal numbers conventionally. For exponents,
add to multiply; subtract to divide.
(3.0 3 102) 3 (2.0 3 104) 5 6.0 3 10214 5 6.0 3 106
(8.0 3 105) / (4.0 3 103) 5 2.0 3 10523 5 2.0 3 102
• After completing the review of scientific notation, go over the algebraic forms
of the two equations given on page 624 of the Student Book. Tell students
that they will need to use these equations to solve problems. Ask, How can you
rearrange n 5 c/v algebraically to solve for v? (v 5 c/n) To solve for c? (c 5 n/v)
• After discussing the algebraic rearrangement of the equation n 5 c/v, go
over Sample Problems 1 and 2, which show the use of the equation in the
given form to calculate the index of refraction in sodium chloride (Sample
Problem 1) and of the rearranged form to calculate the speed of light in
olive oil (Sample Problem 2).
For •Sample Problem 1, c 5 3.00 3 108; vsalt 5 1.96 3 108 are given. Ask,
What do you need to find? (n, the index of refraction for salt) Which equation
can you use? (n 5 c/v) Have students write the equation (n 5 c/v), fill in the
known quantities (n 5 3.00 3 108 / 1.96 3 108), and solve (3.00 3 108 /
1.96 3 108 5 1.53).
• Repeat the process for the second sample problem.
• Go over Table 1 on page 524 of the Student Book. Ask, Do you see any trends
in the index of refraction of different substances? Students should first notice
that all substances are transparent or translucent. A substance cannot
refract light if it is opaque. Second, students may notice that denser
substances seem to have a higher index of refraction. This is only somewhat
true, however, as noted earlier. Oils are not as dense as water (they float
on water) but still have a higher index of refraction than water. Note that
in Table 1, all of the indices of refraction are rounded to the nearest
hundredth.
• To give students additional practice in calculating the speed of light,
distribute BLM 12.4-1 Math Connection: Calculating the Speed of Light in
Various Media. Students will need to look up the indices of refraction of
different media using Table 1 on page 524 of the Student Book.
• The photograph in Figure 1 on page 524 should help students grasp the
concept of light travelling through salt. They may be picturing someone
shining a laser at a pile of table salt. As the photo shows, salt is made up of
transparent crystals. With a narrow enough beam of light, or a large enough
crystal, light can pass through the crystal and be refracted.
NEL
55308_03_ch12_p827-874 pp3.indd 847
Learning Tip
Word Origins
The symbol used to
represent the speed
of light in a vacuum, c,
should not be confused
with the Roman numeral
for 100, which is an
upper case C. The Roman
numeral C comes from the
Latin word centum, which
means 100. The letter c
stands for a Latin word.
The word is celeritás,
which means “velocity.”
Chapter 12 The Refraction of Light
847
11/20/09 6:13:43 PM
Extend and Assess
• Have students compare their results from Section 12.3 "Perform an Activity:
The Refraction of Light Through Different Media" to see how accurate
they were. Then have them use their data to compute the speed of light in
vegetable oil and in water. The information needed to compute these speeds,
the calculations, and the speeds are shown below. Collect students’ work
and compare to the work shown below. Be sure to check that students have
rearranged the equation algebraically as necessary, substituted correct values,
and performed the operations correctly. Two sample solutions are given below.
Vegetable oil: c 5 3.00 3 108 m/s; n 5 1.47
n 5 c/v; v 5 c/n 5 3.00 3 108/1.47 5 2.04 3 108 m/s
Water: c 5 3.00 3 108 m/s; n 5 1.33
n 5 c/v; v 5 c/n 5 3.00 3 108/1.33 5 2.26 3 108 m/s
• Have students complete the Check Your Learning questions on page 525 of
the Student Book.
CHECK
YOUR LEARNING
Suggested Answers
1. (a) The index of refraction for a medium is the ratio of the speed of light in a vacuum to the speed of light in that
medium.
(b) The index of refraction is a dimensionless quantity because it is the ratio of two speeds, which both have the
same units. The common units in the numerator and denominator of the ratio cancel, leaving no units for the
index of refraction.
2. nvinegar 5
3. nsapphire 5
3.00 3 108 m/s ?
5 1.30
2.30 3 108 m/s
3.00 3 108 m/s ?
5 1.78
1.69 3 108 m/s
4. (a) vquartz 5
3.00 3 108 m/s ?
5 2.05 3 108 m/s
1.46
(b) vdiamond 5
3.00 3 108 m/s ?
5 1.24 3 108 m/s
2.42
5. vsolution 5
3.00 3 108 m/s
5 2.01 3 108 m/s
1.49
6. vacetone 5
3.00 3 108 m/s
5 2.21 3 108 m/s
1.36
3.00 3 108 m/s
5 1.36
2.20 3 108 m/s
(b) ethyl alcohol or acetone
7. (a) nunknown 5
8. An answer of 4.0 3 108 m/s is impossible because it exceeds the speed of light in a vacuum (3.00 3 108 m/s),
which is the fastest possible speed for light.
848
Unit E: Light and Geometric Optics
55308_03_ch12_p827-874 pp3.indd 848
NEL
11/20/09 6:13:43 PM
9. (a) The angle of refraction will become smaller.
(b) When the medium in which the refracted light ray travels is changed to glass, the speed of the light is still
greater than in the diamond, but not as great as in air. The refracted ray still bends away from the normal in
the glass, but to a lesser degree than in air.
glass
diamond
10. The speed of light is different from medium to medium, which gives each medium a unique index of refraction. But
the speed of light through a medium is the same regardless of which medium the light passes through first.
DIFFERENTIATED INSTRUCTION
• Challenge visual/spatial learners to create a game in which they show an
image of an incident angle and a refracted angle and players must use the
drawing to identify the “mystery medium” for each problem.
• Have interpersonal learners work in small groups to prepare a presentation of
the material covered in this lesson. Allow students to choose a presentation
format.
ENGLISH LANGUAGE LEARNERS
• Direct students’ attention to the word physicist in the first sentence of
this lesson. Write the suffix –ist on the board. Identify –ist as a suffix that
identifies a person who specializes in an activity. In other words, a physicist
specializes in the study of physics. Have students come up with other
examples, both from science and non-science contexts: artist, chemist,
biologist, cartoonist, psychologist, botanist, and so on. Have students use each
word in a sentence.
NEL
55308_03_ch12_p827-874 pp3.indd 849
At Home
Have students look for
other media in their homes
that will refract light,
such as crystal, plastic,
or amber. They should
then search for resources
that provide the index of
refraction for these media
and calculate the speed of
light through the media.
Chapter 12 The Refraction of Light
849
11/20/09 6:13:43 PM