OpenStax University Physics Volume III
Unit 1: Optics
Chapter 1: The Nature of Light
Page 0 of 18
,OpenStax University Physics Volume III
Unit 1: Optics
Chapter 1: The Nature of Light
University Physics Volume III
Unit 1: Optics
Chapter 1: The Nature of Light
Conceptual Questions
1. Under what conditions can light be modeled like a ray? Like a wave?
Solution
Light can be modeled as a ray when devices are large compared to wavelength, and as a wave
when devices are comparable or small compared to wavelength.
2. Why is the index of refraction always greater than or equal to 1?
Solution
The index of refraction is the ratio of the speed of light in a vacuum to the speed of light in a
medium. Because the former is the fastest that the speed of light can be, this ratio is, by
definition, greater than or equal to 1.
3. Does the fact that the light flash from lightning reaches you before its sound prove that the
speed of light is extremely large or simply that it is greater than the speed of sound? Discuss how
you could use this effect to get an estimate of the speed of light.
Solution
This fact simply proves that the speed of light is greater than that of sound. If one knows the
distance to the location of the lightning and the speed of sound, one could, in principle,
determine the speed of light from the data. In practice, because the speed of light is so great, the
data would have to be known to impractically high precision.
4. Speculate as to what physical process might be responsible for light traveling more slowly in a
medium than in a vacuum.
Solution
answers may vary
5. Using the law of reflection, explain how powder takes the shine off of a person’s nose. What
is the name of the optical effect?
Solution
Powder consists of many small particles with randomly oriented surfaces. This leads to diffuse
reflection, reducing shine.
6. Diffusion by reflection from a rough surface is described in this chapter. Light can also be
diffused by refraction. Describe how this occurs in a specific situation, such as light interacting
with crushed ice.
Solution
Crushed ice has surface segments with a variety of orientations, resulting in refracted rays in
many directions, creating a diffuse effect.
7. Will light change direction toward or away from the perpendicular when it goes from air to
water? Water to glass? Glass to air?
Solution
“toward” when increasing n (air to water, water to glass); “away” when decreasing n (glass to
air)
8. Explain why an object in water always appears to be at a depth shallower than it actually is?
Solution
Rays from underwater objects emerge from water subject to refraction. The observer in air
perceives an apparent location for the source, which is different from the physical location.
Page 1 of 18
,OpenStax University Physics Volume III
Unit 1: Optics
Chapter 1: The Nature of Light
9. Explain why a person’s legs appear very short when wading in a pool. Justify your
explanation with a ray diagram showing the path of rays from the feet to the eye of an observer
who is out of the water.
Solution
A ray from a leg emerges from water after refraction. The observer in air perceives an apparent
location for the source, as if a ray traveled in a straight line. See the dashed ray below.
10. Explain why an oar that is partially submerged in water appears bent.
Solution
Although rays from the parts of the oar above water travel straight to the observer’s eye, rays
from the underwater parts of the oar reach the eye after refraction, making them appear to come
from another direction. This difference in direction appears as a bend in the oar.
11. A ring with a colorless gemstone is dropped into water. The gemstone becomes invisible
when submerged. Can it be a diamond? Explain.
Solution
The gemstone becomes invisible when its index of refraction is the same, or at least similar to,
the water surrounding it. Because diamond has a particularly high index of refraction, it can still
sparkle as a result of total internal reflection, not invisible.
12. The most common type of mirage is an illusion that light from faraway objects is reflected by
a pool of water that is not really there. Mirages are generally observed in deserts, when there is a
hot layer of air near the ground. Given that the refractive index of air is lower for air at higher
temperatures, explain how mirages can be formed.
Solution
A mirage can be regarded as a result of two layers of air: a hot layer near the ground (low n) and
a cool layer above (high n). Rays originating in the cool layer can reflect back up due to an effect
analogous to total internal reflection.
13. How can you use total internal reflection to estimate the index of refraction of a medium?
Solution
One can measure the critical angle by looking for the onset of total internal reflection as the
n2
angle of incidence is varied. c = sin
−1
for n1 n2 can then be applied to compute the
n1
index of refraction.
Page 2 of 18
, OpenStax University Physics Volume III
Unit 1: Optics
Chapter 1: The Nature of Light
14. Is it possible that total internal reflection plays a role in rainbows? Explain in terms of
indices of refraction and angles, perhaps referring to that shown below. Some of us have seen the
formation of a double rainbow; is it physically possible to observe a triple rainbow?
Solution
Total internal reflection is a feature at the back surface of the water droplets that form rainbows
(see the following figure). When the figure is inverted, it illustrates the upper bow in a double
rainbow. Third and higher-order rainbows can be caused by multiple internal reflections; see
http://www.atoptics.co.uk/rainbows/ord34.htm
15. A high-quality diamond may be quite clear and colorless, transmitting all visible wavelengths
with little absorption. Explain how it can sparkle with flashes of brilliant color when illuminated
by white light.
Solution
In addition to total internal reflection, rays that refract into and out of diamond crystals are
subject to dispersion due to varying values of n across the spectrum, resulting in a sparkling
display of colors.
16. How do wave effects depend on the size of the object with which the wave interacts? For
example, why does sound bend around the corner of a building while light does not?
Solution
Compare wavelength with the size of the object. Sound wavelengths are much larger than light
wavelengths, making diffraction around objects the size of buildings observable.
17. Does Huygens’s principle apply to all types of waves?
Solution
yes
Page 3 of 18
Unit 1: Optics
Chapter 1: The Nature of Light
Page 0 of 18
,OpenStax University Physics Volume III
Unit 1: Optics
Chapter 1: The Nature of Light
University Physics Volume III
Unit 1: Optics
Chapter 1: The Nature of Light
Conceptual Questions
1. Under what conditions can light be modeled like a ray? Like a wave?
Solution
Light can be modeled as a ray when devices are large compared to wavelength, and as a wave
when devices are comparable or small compared to wavelength.
2. Why is the index of refraction always greater than or equal to 1?
Solution
The index of refraction is the ratio of the speed of light in a vacuum to the speed of light in a
medium. Because the former is the fastest that the speed of light can be, this ratio is, by
definition, greater than or equal to 1.
3. Does the fact that the light flash from lightning reaches you before its sound prove that the
speed of light is extremely large or simply that it is greater than the speed of sound? Discuss how
you could use this effect to get an estimate of the speed of light.
Solution
This fact simply proves that the speed of light is greater than that of sound. If one knows the
distance to the location of the lightning and the speed of sound, one could, in principle,
determine the speed of light from the data. In practice, because the speed of light is so great, the
data would have to be known to impractically high precision.
4. Speculate as to what physical process might be responsible for light traveling more slowly in a
medium than in a vacuum.
Solution
answers may vary
5. Using the law of reflection, explain how powder takes the shine off of a person’s nose. What
is the name of the optical effect?
Solution
Powder consists of many small particles with randomly oriented surfaces. This leads to diffuse
reflection, reducing shine.
6. Diffusion by reflection from a rough surface is described in this chapter. Light can also be
diffused by refraction. Describe how this occurs in a specific situation, such as light interacting
with crushed ice.
Solution
Crushed ice has surface segments with a variety of orientations, resulting in refracted rays in
many directions, creating a diffuse effect.
7. Will light change direction toward or away from the perpendicular when it goes from air to
water? Water to glass? Glass to air?
Solution
“toward” when increasing n (air to water, water to glass); “away” when decreasing n (glass to
air)
8. Explain why an object in water always appears to be at a depth shallower than it actually is?
Solution
Rays from underwater objects emerge from water subject to refraction. The observer in air
perceives an apparent location for the source, which is different from the physical location.
Page 1 of 18
,OpenStax University Physics Volume III
Unit 1: Optics
Chapter 1: The Nature of Light
9. Explain why a person’s legs appear very short when wading in a pool. Justify your
explanation with a ray diagram showing the path of rays from the feet to the eye of an observer
who is out of the water.
Solution
A ray from a leg emerges from water after refraction. The observer in air perceives an apparent
location for the source, as if a ray traveled in a straight line. See the dashed ray below.
10. Explain why an oar that is partially submerged in water appears bent.
Solution
Although rays from the parts of the oar above water travel straight to the observer’s eye, rays
from the underwater parts of the oar reach the eye after refraction, making them appear to come
from another direction. This difference in direction appears as a bend in the oar.
11. A ring with a colorless gemstone is dropped into water. The gemstone becomes invisible
when submerged. Can it be a diamond? Explain.
Solution
The gemstone becomes invisible when its index of refraction is the same, or at least similar to,
the water surrounding it. Because diamond has a particularly high index of refraction, it can still
sparkle as a result of total internal reflection, not invisible.
12. The most common type of mirage is an illusion that light from faraway objects is reflected by
a pool of water that is not really there. Mirages are generally observed in deserts, when there is a
hot layer of air near the ground. Given that the refractive index of air is lower for air at higher
temperatures, explain how mirages can be formed.
Solution
A mirage can be regarded as a result of two layers of air: a hot layer near the ground (low n) and
a cool layer above (high n). Rays originating in the cool layer can reflect back up due to an effect
analogous to total internal reflection.
13. How can you use total internal reflection to estimate the index of refraction of a medium?
Solution
One can measure the critical angle by looking for the onset of total internal reflection as the
n2
angle of incidence is varied. c = sin
−1
for n1 n2 can then be applied to compute the
n1
index of refraction.
Page 2 of 18
, OpenStax University Physics Volume III
Unit 1: Optics
Chapter 1: The Nature of Light
14. Is it possible that total internal reflection plays a role in rainbows? Explain in terms of
indices of refraction and angles, perhaps referring to that shown below. Some of us have seen the
formation of a double rainbow; is it physically possible to observe a triple rainbow?
Solution
Total internal reflection is a feature at the back surface of the water droplets that form rainbows
(see the following figure). When the figure is inverted, it illustrates the upper bow in a double
rainbow. Third and higher-order rainbows can be caused by multiple internal reflections; see
http://www.atoptics.co.uk/rainbows/ord34.htm
15. A high-quality diamond may be quite clear and colorless, transmitting all visible wavelengths
with little absorption. Explain how it can sparkle with flashes of brilliant color when illuminated
by white light.
Solution
In addition to total internal reflection, rays that refract into and out of diamond crystals are
subject to dispersion due to varying values of n across the spectrum, resulting in a sparkling
display of colors.
16. How do wave effects depend on the size of the object with which the wave interacts? For
example, why does sound bend around the corner of a building while light does not?
Solution
Compare wavelength with the size of the object. Sound wavelengths are much larger than light
wavelengths, making diffraction around objects the size of buildings observable.
17. Does Huygens’s principle apply to all types of waves?
Solution
yes
Page 3 of 18
