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Transcript of fp · PDF filePhysics 202, Lecture 25 Today’s Topics Image Formation Real Image, Virtual...
Physics 202, Lecture 25Today’s Topics
Image Formation Real Image, Virtual Image, and No Image Ray Diagram Images Formed by:
Mirrors (reflection) Concave and Convex
Lenses (refraction) Converging and Diverging
Imaging Imaging: visible object optical device image
opticaldevice
visible object Image
object lights
image lights
No Image: No point to point correspondence
Image Aberration: Poorly focused imaged points
Note: If image can be formed, only two rays per point are necessary
Image Properties
Real Image: image lights actually passthrough image
Virtual Image: image lights appear to have come from the image
Real images can be formed on a screen.
Image properties to be concerned include location, real/virtual, reduced/enlarged,
upright/inverted, similar/distorted,…
Real and Virtual Images
Ray Diagrams If image can be formed, only two rays are necessary
to determine an image point. Useful rays:
Object ray pointing to the center (C) image ray inline with the object ray Object ray parallel to principal axis image ray “pointing to” a focal point (F) Object ray passing through a focal point image ray parallel to principal axis.
principal axis
C
optical device
F
F
O
I
Image Formation Equation and Magnification
Parametersp: object distanceq: image distanceh: object heighth’: image heightM: magnificationf: focal length
�
M = h'h
= − pq
= ff − p
�
1p
+ 1q
= 1f
q = fpp − f
If |M|<1 → Image < ObjectIf |M|>1 → Image > ObjectIf M<0 → Image ↓↑ ObjectIf M>0 → Image ↑↑ Object
Mirr
ors
and
Thin
Len
ses
Image Formed by Flat Mirrors Parametersp: object distanceq: image distanceh: object heighth’:image heightM: magnification
Properties: Image is virtual and behind the mirror. Object distance = image distance (|p|=|q|) Lateral magnification M=1 Image is upright (for upright object) Image has front/back reversal.
1
0,0'
=−==
<>
pq
hhM
qp
Image Formed by Convex Mirror
Quiz 1: Is there another convenient ray to use? Quiz 2:
1. Real or virtual?2. Upright or inverted?3. Enlarged or reduced?
Answer: Virtual, upright (M>0), reduced (|M|<1)
�
f = R /2 < 01p
+ 1q
= 1f
q = fpp − f
< 0
0 < M = − qp
<1
R
Image Formed by Concave Mirrors
Object (O) in between F and Mirror:virtual, upright, enlarged
Object in front of Mirror:real, inverted. Enlarged orreduced, depending on p.
pq
hhM
fqp
Rf
−==
=+
=
'
1112/
Image Formed by Refraction
pq
hhM
Rnn
qn
pn
−==
−=+
'
1221
Closer, not-inverted, reduced, virtual…
R= ∞q= - p(n2/n1)M=-q/p =n2/n1<1
Example: looking at a fish
Thin Lenses Lenses are refractive optical devices with two
spherical sides.
Thin
R1 R2
f1
)11)(1(1
21 RRn
f−−=
Lens maker’s equation
F1,F2: Focal pointsf=f1=f2 Focal length
f2
f>0: convergingf<0: diverging
Converging and Diverging Lenses
sign convention:f<0
sign convention:f>0
Images Formed by Converging Lens
Object (O) is in front of F1 : real, inverted, enlarged or reduced
Object (O) in between F1 and lens: virtual, upright, enlarged.
pq
hhM
fqp
f
−==
=+
>
'
1110
pq
hhM
fqp
f
−==
=+
>
'
1110
Images Formed by Diverging Lenses
Images are always virtual, upright, and reduced
Images Formed by Diverging Lenses
Images are always virtual, upright, and reduced
pq
hhM
fqp
f
−==
=+
<
'
1110
Sign Conventions
>0 <0f concave mirrors
converging lensconvex mirrorsdiverging lens
p object side the other sideq real virtual
M=-q/p upright inverted
Real Virtualmirrors front behindlenses behind front