the wave model · 2019-09-17 · light passes from vacuum (index of refraction n = 1) into water...
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© 2017 Pearson Education, Inc. Slide 32-1
Models of Light
The wave model: Under many circumstances, light exhibits the same behavior as material waves. The study of light as a wave is called wave optics.
The ray model: The properties of prisms, mirrors, and lenses are best understood in terms of light rays. The ray model is the basis of ray optics.
The photon model: In the quantum world, light behaves like neither a wave nor a particle. Instead, light consists of photons that have both wave-like and particle-like properties. This is the quantum theory of light.
Waves and wave fronts
• A wave front is the locus of
all adjacent points at which
the phase of a wave is the same.
• Spherical wave fronts of
sound spread out uniformly
in all directions from a point
source.
• Electromagnetic waves in
vacuum also spread out as
shown here.
© 2016 Pearson Education Inc.
Wave fronts and rays
• It’s often convenient to represent a light wave by rays rather
than by wave fronts.
• A ray is an imaginary line along the direction of travel of the
wave.
• When waves travel in a
homogeneous isotropic
material, the rays are
always straight lines
normal to the wave
fronts.
© 2016 Pearson Education Inc.
Wave fronts and rays
• Far away from a source, where the radii of the spheres have
become very large, a section of a spherical surface can be
considered as a plane, and we have a plane wave.
© 2016 Pearson Education Inc.
© 2017 Pearson Education, Inc. Slide 34-5
Objects can be
either self-luminous,
such as the sun and
lightbulbs, or they
can be reflective.
Most objects are
reflective.
Light from Objects
© 2017 Pearson Education, Inc. Slide 34-6
Rays originate from every point on an object and
travel outward in all directions, but a diagram trying to
show all these rays would be messy and confusing.
To simplify the picture, we use a ray diagram showing
only a few rays.
Ray Diagrams
© 2017 Pearson Education, Inc. Slide 34-7
The law of reflection states that
1. The incident ray and the reflected ray are in the same
plane normal to the surface, and
2. The angle of reflection equals the angle of incidence:
r = i
Reflection
© 2017 Pearson Education, Inc. Slide 34-8
Example 1
A dressing mirror on a closet door is 1.50 m tall. The bottom
is 0.50 m above the floor. A bare lightbulb hangs 1.00 m from
the closet door, 2.50 m above the floor. How long is the streak
of reflected light across the floor?
Diffuse and specular reflection
• Our primary concern in this
chapter will be with specular
reflection from a very smooth
surface such as highly polished
glass or metal (a).
• Scattered reflection from a
rough surface is called diffuse
reflection (b).
• The vast majority of objects in
your environment are visible to
you because they reflect light
in a diffuse manner.
© 2016 Pearson Education Inc.
© 2017 Pearson Education, Inc. Slide 34-10
Consider P, a source of rays that reflect from a mirror.
The reflected rays appear to emanate from P′, the same
distance behind the mirror as P is in front of the mirror.
That is, s′ = s
The Plane Mirror
© 2017 Pearson Education, Inc. Slide 34-11
The Plane Mirror
© 2017 Pearson Education, Inc. Slide 34-12
QuickCheck
You are looking at the image of a
pencil in a mirror. What do you see
in the mirror if the top half of the
mirror is covered with a piece of
dark paper?
A. The full image of the
pencil
B. The top half only of the
pencil
C. The bottom half only of
the pencil
D. No pencil, only the paper
© 2017 Pearson Education, Inc. Slide 34-13
Example 2
If your height is h, what is the shortest mirror on the wall in
which you can see your full image? Where must the top of the
mirror be hung?
© 2017 Pearson Education, Inc. Slide 34-14
In-class Activity #1
A light ray leaves point A in the figure, reflects from the mirror,
and reaches point B. How far below the top edge does the ray
strike the mirror?
© 2017 Pearson Education, Inc. Slide 34-15
Two things happen when a light ray is incident on a
smooth boundary between two transparent materials:
1. Part of the light reflects
from the boundary,
obeying the law of
reflection.
2. Part of the light continues
into the second medium.
The transmission of light
from one medium to
another, but with a change
in direction, is called
refraction.
Refraction
Index of refraction
• The index of refraction of an optical material (also called the
refractive index), denoted by n, is defined as:
• For the case shown here, material b has a larger index of
refraction than material a (nb > na) and the angle θb is smaller
than θa.
© 2016 Pearson Education Inc.
Reflection and refraction: Case 1 of 3
• When a ray passes from one material into another material
having a larger index of refraction and hence a slower wave
speed, the angle θb with the normal is smaller in the second
material than the angle θa in the first.
© 2016 Pearson Education Inc.
Reflection and refraction: Case 2 of 3
• When a ray passes from one material into another material
having a smaller index of refraction and hence a faster wave
speed, the angle θb with the normal is larger in the second
material than the angle θa in the first.
© 2016 Pearson Education Inc.
Reflection and refraction: Case 3 of 3
• In the case of normal incidence, the transmitted ray is not
bent at all.
• In this case θa = 0 and sin θa = 0, so θb is also equal to zero;
the transmitted ray is also normal to the interface.
• θr is also equal to zero, so the reflected ray travels back along
the same path as the incident ray.
© 2016 Pearson Education Inc.
The law of refraction
• This result is also called Snell’s law, after the Dutch scientist
Willebrord Snell (1591–1626).
© 2016 Pearson Education Inc.
Why does the ruler appear to be bent?
• The law of refraction explains why a partially submerged
straight ruler appears bent.
• Light rays coming from below the surface change in direction
at the air–water interface, so the rays appear to be coming
from a position above their actual point of origin.
© 2016 Pearson Education Inc.
Why does the ruler appear to be bent?
© 2016 Pearson Education Inc.
© 2016 Pearson Education, Inc.
Light passes from vacuum (index of refraction n = 1) into water
(n = 1.333). If the incident angle is an acute angle
QuickCheck
A. the refracted angle is greater than the incident angle.
B. the refracted angle is equal to the incident angle.
C. the refracted angle is less than the incident angle.
D. two of A, B, and C are possible, depending on the specific
value of .
© 2016 Pearson Education, Inc.
Light passes from a medium of index of refraction na into a
second medium of index of refraction nb. The angles of
incidence and refraction are respectively. If na < nb,
QuickCheck
A. and the light speeds up as it enters the second
medium.
B. and the light slows down as it enters the second
medium.
C. and the light speeds up as it enters the second
medium.
D. and the light slows down as it enters the second
medium.
© 2017 Pearson Education, Inc. Slide 34-25
A laser beam passing
from medium 1 to
medium 2 is refracted as
shown. Which is true?
QuickCheck
A. n1 < n2
B. n1 > n2
C. There’s not enough
information to compare
n1 and n2.
© 2017 Pearson Education, Inc. Slide 34-26
Indices of Refraction
When light passes from vacuum (index of refraction n = 1)
into water (n = 1.333),
QuickCheck
A. the wavelength increases and the frequency is unchanged.
B. the wavelength decreases and the frequency is
unchanged.
C. the wavelength is unchanged and the frequency increases.
D. the wavelength is unchanged and the frequency
decreases.
Index of refraction and the wave aspects of light
• The frequency f of a wave does not change when passing
from one material to another.
• In any material, v = λf ; since f is the same in any material as
in vacuum and v is always less than the wave speed c in
vacuum, λ is also correspondingly reduced.
• When a wave passes from one material into a second material
the waves get “squeezed” (the wavelength gets shorter) if the
wave speed decreases and get “stretched” (the wavelength
gets longer) if the wave speed increases.
© 2016 Pearson Education Inc.
© 2017 Pearson Education, Inc. Slide 34-29
The figure shows a wave crossing the boundary between two
media, where we’re assuming n2 > n1.
Because the wavelengths differ on opposite sides of the
boundary, the wave fronts can stay lined up only if the waves
in the two media are traveling in different directions.
Refraction
© 2017 Pearson Education, Inc. Slide 34-30
Example 3
In the figure, material a is water and material b is glass with
index of refraction 1.52. The incident ray makes an angle of
60.0º with normal; find the directions of the reflected and
refracted rays.
© 2017 Pearson Education, Inc. Slide 34-31
Example 4
What is the prism’s index of refraction?
© 2017 Pearson Education, Inc. Slide 34-32
Example 5
The wavelength of the red light from a helium-neon laser is
633 nm in air but 474 nm in the aqueous humor inside your
eyeball. Calculate the index of refraction of the aqueous
humor and the speed and frequency of the light in it.
© 2017 Pearson Education, Inc. Slide 34-33
Example 6
Two mirrors are perpendicular to each other as seen in the
figure. A ray traveling in the xy-plane is reflected from one
mirror at P, then the other at Q. What is the ray’s final direction
relative to its original direction?
© 2017 Pearson Education, Inc. Slide 34-34
In-class Activity #2
Find the index of refraction for material X. Also, determine
the angle the light makes with the normal in the air.
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