Waves, Light & Quanta
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Transcript of Waves, Light & Quanta
Waves, Light & QuantaTim Freegarde
Web Gallery of Art; National Gallery, London
2
Circumference of the earth
Eratosthenes of Cyrene (276-195 BC)
• 5000 stadia ~ 5000 x 180m = 900 km
• α = β ~ 1/50 circle
(Tropic of Cancer)
3
Radius astronomicus
Reinerus Gemma-Frisius, Leuven
• measurement of celestial angular distances
4
Camera obscura
• solar eclipse, 24 Jan 1544
Reinerus Gemma-Frisius, Leuven de radio astronomica et geometrica,
1545
5
Pinhole camera
foil screen
pinholeobject
image
6
Rays
• light travels in straight lines
x0 L
a
b
A B C
S
P
S
P
x
• shortest distance between two points
7
The nature of light
light travels between two points by the shortest distance
light travels in straight lines
1.
8
Rays
• light travels in straight lines
x0 L
a
b
A B C
S
P
S
P
x
• shortest distance between two points• equal angles:
P=S
9
Reflection
• light travels in straight lines
x0 L
a
b
S
P
S
P
x
• shortest distance between two points
P
bP
• equal angles:
P=S
10
Reflection at a curved surface
• light travels in straight lines
• shortest distance between two points• equal angles:
P=S
SP
• suppose we design a surface so that all routes are the same length…?
11
Conic sections
SP
directrix
focus
PARABOLA
focus Afocus B
ELLIPSE
SP
12
Concave mirror
• light travels in straight lines
• shortest distance between two points• equal angles:
P=S
SP
• equal times to focus
Rf
13
Lenses and refraction
Hugo of Provence
Nicholas of RouenTommaso da Modena (1325-
1379)Chiesa San Nicolò, Treviso
Ibn al-Haytham ‘Alhazen’(965-1039)
14
Fermat’s principle of least time
• refraction at a plane surfacePierre de Fermat (1601-1665)
x0 L
a
b
A B C
S
P
S
P
x
15
Fermat’s principle of least time
• refraction at a plane surfacePierre de Fermat (1601-1665)
x0 L
a
b
S
P
S
P
x
• light rays follow the path of least time between two points
16
Snell’s law of refraction
• refraction at a plane surface
x0 L
a
b
S
P
S
P
x
• light rays follow the path of least time between two points
• PPSS sinsin
Willebrord Snel van Royen(Leiden, 1580-1626)
17
The nature of light
light travels between two points by the shortest distancelight travels between two points by the quickest route (least time)light travels between two points by the route for which the time taken is a stationary value
light travels in straight lines
1.