Geometrical optics

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Geometrical optics
Physics 135 General Physics II 25/28 February
2005
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Law of reflection
q angle of incidence
q angle of reflection
Planar reflecting surface (mirror)
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Objects and images
Object
Image
Reflected rays appear to come from a point
Rays from point on object reflect from mirror
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Law of refraction
q1 angle of incidence
n1
q2 angle of refraction
n2
( n2 gt n1 in diagram )
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Two simple effects
Total internal reflection
Object underwater appears to be at a shallower
depth
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Thin lenses
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Objects and images
x
y
Three easy rays for ray-tracing
Thin lens equation
magnification
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Reading the signs

• In this diagram
• The object is upstream of the lens.
• The lens is a converging lens.
• The image is a real image through which light
  rays actually pass, and it is downstream of the
  lens.

i, f and o are all positive
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A negative lens
o 50 cm
f -30 cm
i -18.75 cm
m 0.375
Upright, virtual image 37.5 as large as object
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A compound lens system
50 cm
50 cm
150 cm
f 30 cm
f -30 cm
Total magnification
M m m (-1.5) (6.0) - 9.0
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What is going on
Light rays diverge from object.
First lens causes rays to converge.
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What is going on
Light rays diverge from object.
Diverging lens moves image to here.
First lens causes rays to converge.
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Curved mirrors
1. Assume that mirror is a section of a sphere
of radius r
2. Assume that mirrors curve is shallow -- it
is essentially in one plane
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Spherical mirrors
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Spherical mirrors
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x
y
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o
r
x
r - i
y
o - r
i
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(a little algebra)
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Spherical mirror equation
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f 10 cm
i 12.5 cm
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o
r
x
y
i
magnification
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f 10 cm
i 12.5 cm
m - 0.25
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Limiting cases
f ? ? Flat mirror (infinite radius r) o ?
? Parallel incident rays
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Two types of images
Real image i gt 0 , so light rays pass through
image point (in front of mirror) Inverted Virtua
l image i lt 0 , so light rays do not pass through
image point (behind mirror) Upright