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1. General Physics 1/2
Science, Technology, Engineering, and Mathematics
General Physics 2
Science, Technology, Engineering, and Mathematics
Lesson 10.4
Law of Refraction

2. 2
Is the light really
crooked in this photo?

3. 3
Is the branch in this
photo really broken?

4. 4
Do not let your eyes deceive you. Those are just the
applications of refraction.
In this lesson, we will discuss how light refract.

5. 5
Why does light refract?

6. Learning Competencies
At the end of the lesson, you should be able to do the
following:
6
● Apply Snell’s Law (STEM-GP12OPTIVb-15).
● Explain the conditions for total internal
reflection (STEM-GP12OPTIVb-14).

7. Learning Competencies
At the end of the lesson, you should be able to do the
following:
7
● Solve problems involving reflection and
refraction in contexts such as, but not
limited to (polarizing) sunglasses,
atmospheric rainbows, and haloes. (STEM-
GP12OPTIVb-21).

8. Learning Objectives
At the end of the lesson, you should be able to do the
following:
8
● Infer how the refractive index affects the optical
density of a material.
● Explain how light refracts.
● State Snell’s law.

9. Learning Objectives
At the end of the lesson, you should be able to do the
following:
9
● Determine the conditions of total internal
reflection.
● Solve problems related to the refraction and total
internal reflection of light.
● Identify applications of refraction and total
internal reflection in daily life.

10. 10
● Light is refracted when it
travels at a particular angle
(θb) into a medium or
substance that has a
different refractive index, as
shown.
Refraction

11. 11
● Refractive index (n) or index of refraction refers to
the ratio of the speed of light in free space to that of
its speed in a given medium.
● A material’s refractive index is determined by its
optical density, or the “inert tendency” of a
material’s molecules to keep the absorbed energy of
an EM wave in the form of oscillating electrons before
releasing it back as a new disturbance.
Refractive Index

12. 12
● It may also be understood as the measure of the
bending of the light ray as it travels from one medium
to another.
● This is given by:
Refractive Index

13. 13
Common Refractive Indices
Material Refractive Index (n)
vacuum 1.0000
air 1.0003
ice 1.31
water 1.333
ethyl alcohol 1.36
plexiglass 1.51

14. 14
Material Refractive Index (n)
light flint glass 1.58
dense flint glass 1.66
zircon 1.923
diamond 2.417
rutile 2.907
Gallium phosphide 3.50
germanium 4.01-4.05
Common Refractive Indices

15. 15
How does a material’s refractive
index affect its optical density?

16. Remember
16
Optical density must not be confused
with mass density (mass per unit
volume). The more optically dense an
object is, the slower that a wave will
travel through that material.

17. 17
How does reflection and refraction differ?
Refraction of Light

18. 18
● Snell’s law (or the Law of Refraction) describes the
relationship between the angle of incidence θa and
angle of refraction θb as light passes through two
different media.
Snell’s Law

19. 19
● Mathematically, it states that the ratio of the sines of
the angle of incidence θa and angle of refraction θb
(considering both are measured relative to the
normal to the surface) is equivalent to the inverse
ratio of the two indices of refraction.
Snell’s Law

20. 20
Applications of Snell’s Law
Snell’s Law

21. 21
Total Internal Reflection

22. Remember
22
Total internal reflection happens
when a light ray from a material (a) is
incident (or forms an angle of
incidence) on a second material (b) with
a refractive index smaller than that of a,
such that nb> na.

23. 23
Under what conditions does
total internal reflection occurs?

24. Let’s Practice!
24
The speed of light as it passes through an unknown
material is measured at 2.13 10
✕ 8
m/s. Determine
the material’s index of refraction.

25. Let’s Practice!
25
The speed of light as it passes through an unknown
material is measured at 2.13 10
✕ 8
m/s. Determine
the material’s index of refraction.
The refractive index of the unknown material is 1.40.
This is the refractive index of a fluoropolymer.

26. Try It!
26
26
A light ray has a speed of 1.99 ✕ 108
m/s
as it passes through another unknown
medium. What is the material’s index of
refraction?

27. Let’s Practice!
27
A laser beam travelling in air pierces through ethyl
alcohol at an angle of incidence of 25.15o
. Determine
the angle of refraction.

28. Let’s Practice!
28
A laser beam travelling in air pierces through ethyl
alcohol at an angle of incidence of 25.15o
. Determine
the angle of refraction.
The angle of refraction is 18.22o
.

29. Try It!
29
29
Light initially beamed on air hits a
plexiglass at an incidence angle of 40o
.
What angle of refraction will result from
this interaction?

30. Let’s Practice!
30
An incident ray strikes surface AB of a glass prism in
the figure that has a 1.52 index of refraction.
Determine the (a) critical angle and (b) the largest
value that α may have without any light refracted
out at the surface AC of the prism if the prism is
immersed in air.

31. Let’s Practice!
31
An incident ray strikes surface AB of a glass prism in
the figure that has a 1.52 index of refraction.
Determine the (a) critical angle and (b) the largest
value that α may have without any light refracted
out at the surface AC of the prism if the prism is
immersed in air?
The critical angle is 41.13o
.
The largest possible value of
α is 48.86o
.

32. Try It!
32
32
Suppose the prism on the previous
example is now submerged in water.
Solve for the (a) critical angle and the
(b) largest possible of α if total internal
reflection will occur on Surface AC as a
light ray strikes it.

33. Check Your
Understanding
33
Identify what is being referred to in each of the
following statements.
1. Light is refracted when it travels at a particular angle
into a material that has a ____________________ refractive
index.
2. The refractive index refers to the ratio of the speed of
light in ____________________ to that of its speed in
____________________.
3. Free space has a refractive index of ____________________.

34. Check Your
Understanding
34
Identify the refractive index of each of the following
media.
Medium Refractive Index Speed of Light in the
medium
cubic zirconia 1. _________________ 1.39 10
✕ 8
m/s
crown glass 2. _________________ 1.97 ✕ 108
m/s

35. Let’s Sum It Up!
35
● Refraction refers to the bending of light at a
certain angle θb when it passes through a
different medium.
● The refractive index (n) or index of refraction
refers to the ratio of the speed of light in free
space to that of its speed in a given medium.

36. Let’s Sum It Up!
● A material’s refractive index is determined by its
optical density, or the “sluggish tendency” of a
material’s molecules to keep the absorbed
energy of an EM wave in the form of oscillating
electrons before releasing it back as a new
disturbance.
● Snell’s law (or the Law of Refraction) describes
the relationship between the angle of incidence
θa and angle of refraction θb as light passes 36

37. Let’s Sum It Up!
● A light ray passing through a material with a
larger refractive index bends toward the normal
to the surface. The opposite holds true. A ray
oriented along the normal will not bend,
regardless of the composition of the medium.
37

38. Let’s Sum It Up!
● Total internal reflection happens when a light
ray from a material (a) is incident (or forms an
angle of incidence) on a second material (b) with
a refractive index smaller than that of a, such that
nb> na.
38

39. Key Formulas
39
Concept Formula Description
Snell’s Law of
Refraction where
● n is the material’s
refractive index (either
object a or b);
● c is the speed of light in
free space, and
● v is the speed of light
through the material.
Use this formula to
solve for the
refractive index of a
material.

40. Key Formulas
40
Concept Formula Description
Refractive
Index/ Index of
Refraction
where
● n is the material’s
refractive index, and
● θ is the angle of
incidence (a) or
refraction (b) from the
normal to the surface.
Use this relationship to
derive the formulas for
the unknown values
related to Snell’s law.

41. Key Formulas
41
Concept Formula Description
Total Internal
Reflection where
● θcrit is the critical angle
for total internal
reflection;
● nb is the index of
refraction of the second
material, and
● na is the index of
refraction of the first
Use this formula to
solve for the critical
angle when the
conditions of TIR are
observed.

42. Challenge Yourself
42
42
Can reflection and refraction occur at
the same time from a single
interface? Justify your answer.

43. Bibliography
43
Faughn, Jerry S. and Raymond A. Serway. Serway’s College Physics (7th ed). Singapore: Brooks/Cole,
2006.
Giancoli, Douglas C. Physics Principles with Applications (7th ed). USA: Pearson Education, 2014.
Halliday, David, Robert Resnick and Kenneth Krane. Fundamentals of Physics (5th ed). USA: Wiley,
2002.
Knight, Randall D. Physics for Scientists and Engineers: A Strategic Approach (4th ed). USA: Pearson
Education, 2017.
Serway, Raymond A. and John W. Jewett, Jr. Physics for Scientists and Engineers with Modern Physics (9th
ed). USA: Brooks/Cole, 2014.
Walker, James S. Physics (5th ed). USA: Pearson Education, 2017.
Young, Hugh D., Roger A. Freedman, and A. Lewis Ford. Sears and Zemansky’s University Physics with
Modern Physics (13th ed). USA: Pearson Education, 2012.