1
Optics•Electromagnetic spectrum•polarization•Laws of reflection and refraction•TIR
–Images–Mirrors and lenses–Real/virtual, inverted/straight, bigger/smaller
2
hitt
The Sun is about 1.5 X 1011 m away. The time for light to travel this distance is about:
A. 4.5 x 1018 s
B. 8 s
C. 8 min
D. 8 hr
E. 8 yr
3
The index of refraction n encountered by light in any medium except vacuum depends on the wavelength of the light. So if light consisting of different wavelengths enters a material, the different wavelengths will be refracted differently chromatic dispersion
Chromatic Dispersion
33-
Fig. 33-19Fig. 33-20
n2blue>n2red
Chromatic dispersion can be good (e.g., used to analyze wavelength composition of light) or bad (e.g., chromatic aberration in lenses)
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Chromatic Dispersion
33-
Fig. 33-21
Chromatic dispersion can be good (e.g., used to analyze wavelength composition of light)
or bad (e.g., chromatic aberration in lenses)
prism
lens
5
Rainbows
33-
Fig. 33-22
Sunlight consists of all visible colors and water is dispersive, so when sunlight is refracted as it enters water droplets, is reflected off the back surface, and again is refracted as it exits the water drops, the range of angles for the exiting ray will depend on the color of the ray. Since blue is refracted more strongly than red, only droplets that are closer the the rainbow center (A) will refract/reflect blue light to the observer (O). Droplets at larger angles will still refract/reflect red light to the observer.
What happens for rays that reflect twice off the back surfaces of the droplets?
6
For light that travels from a medium with a larger index of refraction to a medium with a smaller medium of refraction n1>n1 2>1, as 1 increases, 2 will reach 90o (the largest possible angle for refraction) before 1 does.
Total Internal Reflection
33-
1 2 2sin sin 90cn n n
Fig. 33-24
n1
n2
Critical Angle:1 2
1
sinc
n
n
When 2> c no light is refracted (Snell’s Law does not have a solution!) so no light is transmitted Total Internal Reflection
Total internal reflection can be used, for example, to guide/contain light along an optical fiber
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Polarization by Reflection
33-
Fig. 33-27
Brewster’s Law
Applications1. Perfect window: since parallel polarization
is not reflected, all of it is transmitted2. Polarizer: only the perpendicular
component is reflected, so one can select only this component of the incident polarization
1 2
1 2 2
90
sin sin
sin sin 90 cos
B r
B r
B B B
n n
n n n
Brewster Angle:1 2
1
tanB
n
n In which direction does light reflecting
off a lake tend to be polarized?
When the refracted ray is perpendicular to the reflected ray, the electric field parallel to the page (plane of incidence) in the medium does not produce a reflected ray since there is no component of that field perpendicular to the reflected ray (EM waves are transverse).
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Chapter 34
One of the most important uses of the basic laws governing light is the production of images. Images are critical to a variety of fields and industries ranging from entertainment, security, and medicine
In this chapter we define and classify images, and then classify several basic ways in which they can be produced.
Images
34-
9
Image: a reproduction derived from light
Real Image: light rays actually pass through image, really exists in space (or on a screen for example) whether you are looking or not
Virtual Image: no light rays actually pass through image. Only appear to be coming from image. Image only exists when rays are traced back to perceived location of source
Two Types of Images
34-
object lensreal image
object mirror virtual image
10
Light travels faster through warm air warmer air has smaller index of refraction than colder air refraction of light near hot surfaces
For observer in car, light appears to be coming from the road top ahead, but is really coming from sky.
A Common Mirage
34-
Fig. 34-1
11
Plane mirror is a flat reflecting surface.
Plane Mirrors, Point Object
34-
Fig. 34-2
Fig. 34-3
Ib Ob
Identical triangles
Plane Mirror: i p
Since I is a virtual image i < 0
12
Each point source of light in the extended object is mapped to a point in the image
Plane Mirrors, Extended Object
34-
Fig. 34-4 Fig. 34-5
13
Your eye traces incoming rays straight back, and cannot know that the rays may have actually been reflected many times
Plane Mirrors, Mirror Maze
34-
Fig. 34-6
1
23
4
56
78
9
12
34
56
78
9
14
Plane mirror Concave Mirror
1. Center of Curvature C:
in front at infinity in front but closer
2. Field of view
wide smaller
3. Image
i=p |i|>p
4. Image height
image height = object height image height > object height
34-Fig. 34-7
Plane mirror Convex Mirror
1. Center of Curvature C:
in front at infinity behind mirror and closer
2. Field of view
wide larger
3. Image
i=p |i|<p
4. Image height
image height = object height image height < object height
Spherical Mirrors, Making a Spherical Mirror
concave
plane
convex
15
Spherical Mirrors, Focal Points of Spherical Mirrors
34-
Fig. 34-8
concave convex
Spherical Mirror:1
2f r
r > 0 for concave (real focal point)r < 0 for convex (virtual focal point)
16
Start with rays leaving a point on object, where they intersect, or appear to intersect marks the corresponding point on the image.
Images from Spherical Mirrors
34-
Fig. 34-9
Real images form on the side where the object is located (side to which light is going). Virtual images form on the opposite side.
Spherical Mirror:1 1 1
p i f Lateral Magnification:
'hm
h
Lateral Magnification:i
mp
17
Locating Images by Drawing Rays
34-
Fig. 34-10
1. A ray parallel to central axis reflects through F2. A ray that reflects from mirror after passing through F, emerges parallel to central axis3. A ray that reflects from mirror after passing through C, returns along itself4. A ray that reflects from mirror after passing through c is reflected symmetrically about the
central axis
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Proof of the magnification equation
34-
Fig. 34-10
Similar triangles (are angles same)
, ,
(magnification)
de cd decd i ca p m
ab ca abi
mp
19
Spherical Refracting Surfaces
34-
Fig. 34-11
Real images form on the side of a refracting surface that is opposite the object (side to which light is going). Virtual images form on the same side as the object.
Spherical Refracting Surface: 1 2 2 1n n n n
p i r
When object faces a convex refracting surface r is positive. When it faces a concave surface, r is negative. CAUTION: Reverse of of mirror sign convention!
2034-
Fig. 34-13
Converging lens
Diverging lens
Thin Lens:1 1 1
f p i Thin Lens in air:
1 2
1 1 11n
f r r
Lens only can function if the index of the lens is different than that of its surrounding medium
Thin Lenses
21
Images from Thin Lenses
34-
Fig. 34-14
Real images form on the side of a lens that is opposite the object (side to which light is going). Virtual images form on the same side as the object.
22
Locating Images of Extended Objects by Drawing Rays
34-
Fig. 34-15
1. A ray initially parallel to central axis will pass through F22. A ray that initially passes through F1, will emerge parallel to central axis3. A ray that initially is directed toward the center of the lens will emerge from the lens
with no change in its direction (the two sides of the lens at the center are almost parallel)
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Two Lens System
34-
1. Let p1 be the distance of object O from Lens 1. Use equation and/or principle rays to determine the distance to the image of Lens 1, i1.
2. Ignore Lens 1, and use I1 as the object O2. If O2 is located beyond Lens 2, then use a negative object distance p1. Determine i2 using the equation and/or principle rays to locate the final image I2.
Lens 1 Lens 2
p1
OI1
i1
O2
p2
I2
i2
1 2The net magnification is: M m m
24
Optical Instruments, Simple Magnifying Lens
34-
Fig. 34-17
Can make an object appear larger (greater angular magnification) by simply bringing it closer to your eye. However, the eye cannot focus on objects closer that the near point pn~25 cmBIG & BLURRY IMAGE
A simple magnifying lens allows the object to be placed close by making a large virtual image that is far away.
'
and '25 cm
m
h h
f
Simple Magnifier:
25 cmm
f
Object at F1
2534-
Fig. 34-18
Optical Instruments, Compound Microscope
obob
ob ey
since and
25 cm magnification compounded (microscope)
i sm i s p f
p f
sM mm
f f
I close to F1’O close to F1
Mag. Lens
26
Optical Instruments, Refracting Telescope
34-
Fig. 34-19
eyob ey
ob ob ey
ob
ey
' ' , ,
(telescope)
h hm
f f
fm
f
I close to F2 and F1’
Mag. Lens
27
Three Proofs, The Spherical Mirror Formula
34-
Fig. 34-20
and 2
1
2
,
12
2
1 1 1
2
22
ac ac ac ac
cO p cC r
ac ac
CI i
f r
ac ac ac
p i
r f
pf i f
28
Three Proofs, The Refracting Surface Formula
34-
Fig. 34-21
1 1 2 2
1 1 2 2 1 2
1 2
1 2
1 2 2 1
1 2 2
1 2 2 1
1
sin sin
if and are small
and
; ;
n n n n
ac ac acn n n
n n
n n
n
np
n
ac ac ac
p r i
n n n n
p i
i
r
r
2934-
Fig. 34-22
1 2 2 1
1 2
where 1 and
'' '
1 1 ; if small
1 1 Eq. 34-22
' ' '
1 1 Eq. 34-25
' '' ''
Eq. 34-22 Eq. 34
' '' ''1 1 1 1 1 1 1 1
1 1' '' ' '
-25' ' ''
n n n n
p i r
n n n
p i L
n nL
i L i r
n np i r r p
n n
p i r
n n
i r
i i
r
r
Three Proofs, The Thin Lens Formulas
30
hitt
A point source emits electromagnetic energy at a rate of 100W. The intensity 10 m from the
source is:
A. 10 W/m2
B. 1.6 W/m2
C. 1 W/m2
D. 0:024 W/m2
E. 0:080 W/m2