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Physics 2102
Jonathan
Dowling
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Lecture 36: FRI 17 APR
34.1–4: Geometrical optics
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Geometrical Optics
• “Geometrical” optics (rough approximation): light rays
(“particles”) that travel in straight lines.
• “Physical” Classical optics (good approximation):
electromagnetic waves which have amplitude and phase that
can change.
• Quantum Optics (exact): Light is BOTH a particle (photon) and
a wave: wave-particle duality.
Plane Mirrors
Light rays reflect on a plane mirror, and
produce a virtual image behind the
mirror.
What’s a virtual image? It means the
light rays are NOT coming from a real
point, there is no light where the image
appears.
object
image
i= -p for a plane mirror
Ray Tracing Plane (Flat) Mirror
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• Draw Two Rays From Object to Point on Mirror.
• Draw Perpendicular Line to Mirror From Each Point.
• Use i=r To Draw Reflected Rays to Eye.
• Extend Reflected Rays Behind Mirror to Find Virtual Image
Ray Tracing Plane (Flat) Mirror
m = ho/hi = +1
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hi=+ho
ho
= –do
Image distance is minus Object distance, do = –di , means
image is behind (minus) the mirror and | do |= |di| means image
is behind mirror same distance object is in front.
Virtual image means no light actually is at the image location
(optical illusion).
Magnification m = +1 means image has same height as object
(|m|=1) and image is right-side up (m is plus).
Spherical mirrors
• Focal point is at half the curvatuire radius: f= - r/2 .
•Rays parallel to the axis, reflect through the focal point.
• Rays hitting the mirror after going to the focal point, emerge parallel.
• Rays going through the center of curvature, reflect back on themselves.
Concave mirrors: r > 0
Convex mirrors: r < 0
Images from
spherical mirrors
Consider an object placed between the focal point
and the mirror. It will produce a virtual image
behind the mirror.
When the object is at the focal point the image is
produced at infinity.
If the object is beyond the focal point, a real
image forms at a distance i from the mirror.
1 1 1
 
p i f
i
m
p
Check the signs!!
lateral
magnification
Ray Tracing Concave Mirror: Image Outside Focal Point
• Horizontal Ray Bounces Through Focal Point
• Ray Through Focal Point Bounces into Horizontal
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• Ray Through Center Bounces Straight Back At’cha!
• Rays Cross at Image Point
• Image is Real (Light At Image), Inverted, and Shrunk (m=ho/hi is minus
and |m|< 1) and do and di are both positive (to left)
Ray Tracing Concave Mirror: Image Inside Focal Point
• Horizontal Ray Bounces Through Focal Point
• Ray Through Focal Point Bounces into Horizontal
• Ray Through Center Bounces Straight Back At’cha!
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• Project Behind Mirror to Cross at Virtual Image
• Image is Virtual (no light), Upright, and Enlarged (m=ho/hi is plus and > 1)
And do = + and di = – are on opposite sides of mirror.
Ray Tracing Convex Mirror
• Horizontal Ray Bounces Into Line of Focal Point
• Ray Towards Focal Point Bounces into Horizontal
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• Ray Towards Center Bounces Straight Back At’cha!
• Project Rays Behind Mirror Cross at Virtual Image
• Image is Virtual (no light), Upright, and Shrunk (m=ho/hi is plus and < 1)
And do = + and di = – are on opposite sides of mirror.
Example
An object 2cm high is located 10cm from a convex mirror with a radius of
curvature of 10cm. Locate the image, and find its height.
Focal length: f= r/2= -10cm/2= -5cm.
Image position: 1/i=1/f-1/p= -1/5cm –1/10cm= -3/10cm
i= - 10/3cm = -3.33 cm: the image is virtual.
Magnification: m= -i/p= - (-3.33cm)/(10cm)=+0.33 (upright, smaller).
If the object image is 2cm, the image height is 0.33 x 2cm=0.67 cm.
Newton’s Reflecting Telescope
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Hubble, Hubble, Toil and
Trouble
Hubble mirror screw up: The central
region of the mirror was flatter than it
should be - by just one-fiftieth of the
width of a human hair. This is equivalent
to only four wavelengths of visible light,
but it was enough. One insider said that
the Hubble mirror was "very accurate,
very accurately the wrong shape".
A star seen with a ground
telescope and with “old” Hubble
The same star seen
with the “new” Hubble
Before and after...
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