Download Lecture20_InternalReflect

Physics 7E
Prof. D. Casper
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• Chapter 32 HW is due Thursday, 7 am
• Discussion Thursday (Chapter 33)
• Reading
• Friday: Veterans’ Day!
• Next Monday: Chapter 33.6 – 33.7
• Next Wednesday: Chapter 34.1 – 34.2
• Chapter 33 HW is due next Thursday (Nov. 17)
Wave Fronts and the Ray Model
A wave front is a set of adjacent
points at which the phase of the wave
is the same
• Crests are wavefronts
• Troughs are wavefronts too
Rays are imaginary lines along the
wave’s direction of travel
For waves traveling in a homogeneous
material, rays are straight lines normal
to the wave fronts
(At a boundary between materials, the
direction of rays may change)
Point source emitting spherically
expanding wave fronts (crests)
Reflection and Refraction
Just as a wave on a string can be
partially reflected and partially
transmitted at a boundary, so can
electromagnetic waves
The transmitted part of the light
wave is called “refraction” because
unlike the one-dimensional wave on
the string, it is bent into a different
direction
Law of Reflection
Specular reflection (reflection from a
smooth surface) obeys very simple laws:
• Incident and reflected rays line in same
plane with normal to surface
• Angle of reflection = Angle of incidence
• 𝜃𝑟 = 𝜃𝑎
Specular
reflection
Diffuse
reflection
Index of Refraction
Light always moves at the same, fixed speed in vacuum: 𝑐
In a material, the speed of light can and will be different (smaller): 𝑣
The index of refraction 𝑛 specifies the speed of light in a given material:
𝑐
𝑣=
𝑛
𝑛 = 1 for vacuum, and 𝑛 > 1 for materials
For air, 𝑛 = 1.00029, which we usually approximate as 𝑛 = 1
The frequency of waves is the same across a boundary; the wavelength
changes:
𝜆vacuum
𝜆=
𝑛
Q33.1
When light passes from vacuum (index of refraction n = 1) into water (n = 1.333),
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.
E. both the wavelength and the frequency change.
A33.1
When light passes from vacuum (index of refraction n = 1) into water (n = 1.333),
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.
E. both the wavelength and the frequency change.
Law of Refraction (Snell’s Law)
The law of refraction at a boundary depends on the indices of refraction of
the two materials:
𝑛1 sin 𝜃1 = 𝑛2 sin 𝜃2
Note the incident and refracted rays are also in the same plane as the normal
The angles of incidence and reflection are measured from the normal
Q33.2
Light passes from air (index of refraction n = 1) into water (n = 1.333).
If the incident angle qa is in the range 0° < qa < 90°,
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. the answer depends on the specific value of qa .
A33.2
Light passes from air (index of refraction n = 1) into water (n = 1.333).
If the incident angle qa is in the range 0° < qa < 90°,
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. the answer depends on the specific value of qa .
A Bent Ruler?
Index of Refraction
Index of Refraction varies for different materials
Always 1 for vacuum and ~1 for gases
Worth remembering
• Water: 𝑛 = 1.333
• Glasses: 𝑛 = 1.5 − 1.8
No Refraction?
Suppose we have light in glass (𝑛𝑎 = 1.55)
incident on a boundary with water (𝑛𝑏 = 1.33)
Because 𝑛𝑏 < 𝑛𝑎 , the angle 𝜃𝑏 > 𝜃𝑎
For some value 𝜃𝑎 = 𝜃𝑐𝑟𝑖𝑡 , 𝜃𝑏 = 90∘
For incident angles 𝜃𝑎 > 𝜃𝑐𝑟𝑖𝑡 , there is no
angle 𝜃𝑏 which can satisfy the Law of
Refraction, and there is no refracted ray
We say total internal reflection occurs at the
boundary
Internal Reflection
Internal reflection creates a striking effect underwater: the world
above the water’s surface is compressed into a cone.
Outside that cone, the water’s surface acts like a mirror
Critical Angle
The critical angle corresponds to
an angle of refraction of 90∘ :
𝑛𝑎 sin 𝜃𝑐 = 𝑛𝑏 sin 90∘ = 𝑛𝑏
So
𝑛𝑏
sin 𝜃𝑐 =
𝑛𝑎
This angle only exists if 𝑛𝑎 > 𝑛𝑏
Total Internal Reflection Applications
Critical Angle?
The Critical Angle in total internal reflection occurs when incident light
on a surface is …
A. Refracted at 90∘ to the surface
B. Reflected at 90∘ to the surface
C. Refracted at 90∘ to the normal
D. Reflected at 90∘ to the normal
E. Totally absorbed
Dispersion
In real materials, the index of refraction
depends on the wavelength (or frequency)
This dependence is called “dispersion” and
results in light of different colors being
refracted differently
Most noticeable when starting with a mixture
of different colors (e.g. white light)
Dispersion in a Prism
Dispersion in Rainbows