Chapter 30 Reflection and Refraction. Geometric Optics and Ray Approximation Light travels in a...
-
Upload
bartholomew-greer -
Category
Documents
-
view
219 -
download
0
Transcript of Chapter 30 Reflection and Refraction. Geometric Optics and Ray Approximation Light travels in a...
Chapter 30
Reflection and Refraction
Geometric Optics and Ray Approximation
• Light travels in a straight-line path in a homogeneous medium until it encounters a boundary between two different media
• The ray approximation is used to represent beams of light – a ray of light is an imaginary line drawn along the direction of travel of the light beams
• A wave front is a surface passing through points of a wave that have the same phase
• The rays, corresponding to the direction of the wave motion, are perpendicular to the wave front
• Light travels in a straight-line path in a homogeneous medium until it encounters a boundary between two different media
• The ray approximation is used to represent beams of light – a ray of light is an imaginary line drawn along the direction of travel of the light beams
• A wave front is a surface passing through points of a wave that have the same phase
• The rays, corresponding to the direction of the wave motion, are perpendicular to the wave front
Geometric Optics and Ray Approximation
Specular Reflection
• Specular reflection is reflection from a smooth surface
• The reflected rays are parallel to each other
• All reflection in this chapter is assumed to be specular
Diffuse Reflection
• Diffuse reflection is reflection from a rough surface
• The reflected rays travel in a variety of directions
• Diffuse reflection makes the dry road easy to see at night
Law of Reflection• The normal is a line perpendicular
to the surface at the point where the incident ray strikes the surface
• The incident ray makes an angle of θ1 with the normal and the reflected ray makes an angle of θ1’ with the normal
• The angle of reflection is equal to the angle of incidence:
θ1= θ1’
Refraction of Light
• When a ray of light traveling through a transparent medium encounters a boundary leading into another transparent medium, part of the ray is reflected and part of the ray enters the second medium
• The ray that enters the second medium is refracted – bent at the boundary
Refraction of Light
• The incident ray, the reflected ray, the refracted ray, and the normal all lie on the same plane
• The angle of refraction, θ2, depends on the properties of the medium and the angle of incidence
• The path of the light through the refracting surface is reversible
constv
v
1
2
1
2
sin
sin
Refraction of Light
• Ray is the incident ray
• Ray is the reflected ray
• Ray is refracted into the crystal
• Ray is internally reflected in the crystal
• Ray is refracted as it enters the air from the crystal
Refraction of Light
• Light may refract into a material where its speed is lower
• The angle of refraction is less than the angle of incidence so the ray bends toward the normal
constv
v
1
2
1
2
sin
sin
Refraction of Light
• Light may refract into a material where its speed is higher
• The angle of refraction is greater than the angle of incidence so the ray bends away from the normal
constv
v
1
2
1
2
sin
sin
The Index of Refraction• When light passes from one medium to another, it is
refracted because the speed of light is different in the two media
• The index of refraction, n, of a medium can be defined
• n is a unitless ratio
• For a vacuum, n = 1 whereas for other media, n > 1
speed ofl ight in a vacuum cn
speed ofl ight in a medium v
The Index of Refraction
• The wavefronts do not pile up, nor are created or destroyed at the boundary
• Therefore, as light travels from one medium to another, its frequency does not change
• Both the wave speed and the wavelength do change
The Index of Refraction
v1 = ƒ λ1 v2 = ƒ λ2
• The ratio of the indices of refraction of the two media can be expressed as various ratios
1 1 1 2
2 2 12
cv n n
cv nn
Snell’s Law of Refraction
n1 sin θ1 = n2 sin θ2
1 1 1 2
2 2 12
cv n n
cv nn
Willebrord Snelvan Royen
1580 – 1626
1
2
1
2
sin
sin
v
v
2
2
1
1
sinsin
Chapter 30Problem 35
You’re standing 2.3 m horizontally from the edge of a 4.5-m-deep lake, with your eyes 1.7 m above the water’s surface. A diver holding a flashlight at the lake bottom shines the light so you can see it. If the light in the water makes a 42° angle with the vertical, at what horizontal distance is the diver from the edge of the lake?
Atmospheric Refraction• There are many interesting results
of refraction in the atmosphere
• At sunsets, light rays from the sun are bent as they pass into the atmosphere
• It is a gradual bend because the light passes through layers of the atmosphere, and each layer has a slightly different index of refraction
• The Sun is seen to be above the horizon even after it has fallen below
Atmospheric Refraction• A mirage can be observed when the air above the
ground is warmer than the air at higher elevations
• The rays in path B are directed toward the ground and then bent by refraction
• The observer sees both an upright and an inverted image
Atmospheric Refraction
Polarization by Reflection
• When an unpolarized light beam is reflected from a surface, the reflected light can be completely polarized, partially polarized, or unpolarized
• It depends on the angle of incidence
• If the angle is 0° or 90°, the reflected beam is unpolarized
• For angles between this, there is some degree of polarization
• For one particular angle, the beam is completely polarized
Polarization by Reflection
• The angle of incidence for which the reflected beam is completely polarized is called the polarizing (or Brewster’s) angle, θp
• Brewster’s Law relates the polarizing angle to the index of refraction for the material
sintan
cosp
pp
n
Sir David Brewster
1781 – 1868
18090 2 p p 902
2
1
sin
sin
n2sin
sin
p
p
p
cos
sin
Total Internal Reflection
• Total internal reflection can occur when light attempts to move from a medium with a high index of refraction to one with a lower index of refraction
• Ray 5 shows internal reflection
Critical Angle• A particular angle of incidence (critical
angle) will result in an angle of refraction of 90°
• For angles of incidence greater than the critical angle, the beam is entirely reflected at the boundary
• This ray obeys the Law of Reflection at the boundary
21 2
1
sin C
nfor n n
n
Chapter 30Problem 48
Find a simple expression for the speed of light in a material in terms of c and the critical angle at an interface between the material and vacuum.
Fiber Optics
• Utilizes internal reflection
• Plastic or glass rods are used to “pipe” light from one place to another
• Applications include diagnosis and correction of medical problems, telecommunications, etc.
Dispersion• The index of refraction in anything except
a vacuum depends on the wavelength of the light
• This dependence of n on λ is called dispersion
• Snell’s Law indicates that the angle of refraction made when light enters a material depends on the wavelength of the light
• The index of refraction for a material usually decreases with increasing wavelength
Refraction in a Prism• The amount the ray is bent away from its original
direction is called the angle of deviation, δ
• Since all the colors have different angles of deviation, they will spread out into a spectrum: violet deviates the most and red deviates the least
Spectroscopy
• A prism spectrometer uses a prism to cause the wavelengths to separate (to study wavelengths emitted by a light source)
• All hot, low pressure gases emit their own characteristic spectra with the particular wavelengths emitted by a gas serving as “fingerprints” of that gas
• Spectral analysis: identification of molecules, minerals, elements in distant stars, etc.
The Rainbow• A ray of light strikes a drop of water
in the atmosphere and undergoes both reflection and refraction
• First refraction at the front of the drop: violet light will deviate the most and red – the least
• At the back surface the light is reflected and refracted again as it returns to the front surface and moves into the air
• The rays leave the drop at various angles
The Rainbow• If a raindrop high in the sky is observed, the red ray is
seen
• A drop lower in the sky would direct violet light to the observer
• The other colors of the spectra lie in between the red and the violet
Answers to Even Numbered Problems
Chapter 30:
Problem 12
(a) 4
Answers to Even Numbered Problems
Chapter 30:
Problem 36
1.3 m
Answers to Even Numbered Problems
Chapter 30:
Problem 38
42°