why is the sky blue? how do rainbows work?. refraction of light
TRANSCRIPT
Why is the sky blue? How do rainbows work?
Refraction Of Light
Specular reflection is reflection from a smooth surface
The reflected rays are parallel to each other
All reflection in this text is assumed to be specular
Diffuse reflection is reflection from a rough surface
The reflected rays travel in a variety of directions
Diffuse reflection makes the road easy to see at night
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
Ray is the incident ray
Ray is the reflected ray
Ray is refracted into the lucite
Ray is internally reflected in the lucite
Ray is refracted as it enters the air from the lucite
Light is refracted because the speed of light varies in different media◦ nair = 1.00◦ nglass = 1.458 -1.66◦ ndiamond = 2.419
The speed of light varies in different media because of varying time lags in absorption and re-emission of light due to electronic structure
The index of refraction, n, of a medium can be defined
For a vacuum, n = 1 For other media, n > 1 n is a unitless ratio When n>1, light slows down to maintain
frequency
v
c
mediumainlightofspeed
vacuumainlightofspeedn
Chapter 14
Chapter 14
Chapter 14
Discovered experimentally
n1 sin θ1 = n2 sin θ2 ◦ θ1 is the angle of incidence
30.0° in this diagram
◦ θ2 is the angle of refraction
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◦ Red deviates the least
Fig. 22.16, p.697
The index of refraction for a material usually decreases with increasing wavelength
Violet light refracts more than red light when passing from air into a material
This phenomena is also known as dispersion
A thin lens consists of a piece of glass or plastic, ground so that each of its two refracting surfaces is a segment of either a sphere or a plane
Lenses are commonly used to form images by refraction in optical instruments
These are examples of converging lenses
They have positive focal lengths
They are thickest in the middle
These are examples of diverging lenses
They have negative focal lengths
They are thickest at the edges
The focal length, ƒ, is the image distance that corresponds to an infinite object distance◦ This is the same as for mirrors
A thin lens has two focal points, corresponding to parallel rays from the left and from the right◦ A thin lens is one in which the distance between
the surface of the lens and the center of the lens is negligible
The parallel rays pass through the lens and converge at the focal point
The parallel rays can come from the left or right of the lens
The parallel rays diverge after passing through the diverging lens
The focal point is the point where the rays appear to have originated
Chapter 14
The equations can be used for both converging and diverging lenses◦ A converging lens has a positive focal length◦ A diverging lens has a negative focal length
The geometric derivation of the equations is very similar to that of mirrors
f
1
q
1
p
1
p
q
h
'hM
Lens TypeLens Type ObjectObject
Beyond Beyond Focal Focal PointPoint
Object Object
At At
Focal Focal PointPoint
ObjectObject
BetweenBetween
Focal Focal PointPoint
And LensAnd LensConvergingConverging
(convex)(convex)Real Real
Inverted Inverted Reduced Reduced ImageImage
No Image No Image FormedFormed
Erect Erect Virtual Virtual
Magnified Magnified ImageImage
DivergingDiverging
(concave)(concave)Virtual Virtual Erect Erect
Reduced Reduced ImageImage
Virtual Virtual Erect Erect
Reduced Reduced ImageImage
Virtual Virtual Erect Erect
Reduced Reduced ImageImage
QuantityQuantity Positive Positive WhenWhen
Negative Negative WhenWhen
Object location (p)Object location (p) Object is in front of Object is in front of the lensthe lens
Object is in back of Object is in back of the lensthe lens
Image location (q)Image location (q) Image is in back of Image is in back of the lens (real the lens (real image)image)
Image is in front of Image is in front of the lens (virtual the lens (virtual image)image)
Image height (h’)Image height (h’) Image is uprightImage is upright Image is invertedImage is inverted
MagnificationMagnification Image is uprightImage is upright Image is invertedImage is inverted
Focal length (f)Focal length (f) Converging lensConverging lens Diverging lensDiverging lens
The image is real The image is inverted
The image is virtual The image is upright
The image is virtual The image is upright
Ray diagrams are essential for understanding the overall image formation
Three rays are drawn◦ The first ray is drawn parallel to the first principle
axis and then passes through (or appears to come from) one of the focal lengths
◦ The second ray is drawn through the center of the lens and continues in a straight line
◦ The third ray is drawn from the other focal point and emerges from the lens parallel to the principle axis
There are an infinite number of rays, these are convenient
A ray of light strikes a drop of water in the atmosphere
It undergoes both reflection and refraction◦ First refraction at the front of the drop
Violet light will deviate the most Red light will deviate the least
A prism spectrometer uses a prism to cause the wavelengths to separate
The instrument is commonly used to study wavelengths emitted by a light source
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
When the incident angle is equal to the When the incident angle is equal to the critical angle, total internal reflection occurscritical angle, total internal reflection occurs
A particular angle of incidence will result in an angle of refraction of 90°
This angle of incidence is called the critical angle
n1sinθc=n2sin90Therefore:
sinθc= n2
n1Calculate the critical angle for a Plastic light guide, n=1.49
An application of internal reflection
Plastic or glass rods are used to “pipe” light from one place to another
Applications include◦ medical use of fiber
optic cables for diagnosis and correction of medical problems
◦ Telecommunications Internet
◦ Dash board lighting
Fig. 22.29, p.705
Huygen assumed that light is a form of wave motion rather than a stream of particles
Huygen’s Principle is a geometric construction for determining the position of a new wave at some point based on the knowledge of the wave front that preceded it
All points on a given wave front are taken as point sources for the production of spherical secondary waves, called wavelets, which propagate in the forward direction with speeds characteristic of waves in that medium◦ After some time has elapsed, the new position
of the wave front is the surface tangent to the wavelets
At t = 0, the wave front is indicated by the plane AA’
The points are representative sources for the wavelets
After the wavelets have moved a distance cΔt, a new plane BB’ can be drawn tangent to the wavefronts
The inner arc represents part of the spherical wave
The points are representative points where wavelets are propagated
The new wavefront is tangent at each point to the wavelet
All hot, low pressure gases emit their own characteristic spectra
The particular wavelengths emitted by a gas serve as “fingerprints” of that gas
Some uses of spectral analysis◦ Identification of molecules◦ Identification of elements in distant stars◦ Identification of minerals
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 when light enters a material depends on the wavelength of the light
The Law of Reflection can be derived from Huygen’s Principle
AA’ is a wave front of incident light
The reflected wave front is CD
Triangle ADC is congruent to triangle AA’C
θ1 = θ1’ This is the Law of
Reflection
In time Δt, ray 1 moves from A to B and ray 2 moves from A’ to C
From triangles AA’C and ACB, all the ratios in the Law of Refraction can be found◦ n1 sin θ1 = n2 sin θ2
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 bent at the boundary◦ This bending of the ray is called refraction
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 Total internal reflection occurs only when
light attempts to move from a medium of higher index of refraction to a medium of lower index of refraction
Fig. 22.12, p.694