Transcript L2: Mirrors and lenses, Human eye, corrective optics, optical devices. (Ch. 34 )

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7/24/2016
Lecture II
1
Lenses, mirrors and human eye
Physics 123, Spring, 2006
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Lecture II
2
Concepts
• Concave and convex mirrors
– Focus
• Converging and diverging lenses
– Lens equation
• Eye as an optical instrument
• Far and near points
• Corrective lenses System of lenses
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3
Spherical mirrors
• Convex mirror bulges out – diverges light
• Concave mirror caves in – converges light
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4
Focus
• Parallel beam of light (e.g. from a very distant object) is
converged in 1 point – focal point F
• Distance from the mirror to F is called focal distance, or
focus
f =r/2
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5
Ray tracing
3 Easy rays:
1. Parallel  through focus
2. Through focus  parallel
(reversible rays)
3. Through the center of
curvature C  itself
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6
Magnification
• h0 – object height
– h0>0 - always
• hi – image height
– hi>0 – upright image
– hi<0 – inverted image
• m=hi/h0 - magnification
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hi
di
m

ho
do
|m|>1 –image larger than object
|m|<1 –image smaller than object
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7
Mirror equation
• d0 – distance to object
– d0>0 - always
• di – distance to image
1 1 1
 
do di
f
– di>0 – real image
– di<0 – virtual image
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Convex mirror
• Virtual focus – parallel
beam focuses behind the
mirror:
f<0
• Same rules for ray
tracing.
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Sign convention for mirrors
d0>0
h0>0
di>0 – real image
hi>0 – upright image
f>0 – concave mirror
hi
di
m

ho
do
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di<0 - virtual image
hi<0 - inverted image
f<0 – convex mirror
•hi>0di<0 – upright image is always virtual
•hi<0di>0 – inverted image is always real
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10
Images in curved mirrors
•
•
•
•
Concave mirror
d0>r – (real, inverted), smaller
r>d0>f – (real, inverted), larger
d0<f – (virtual, upright), larger
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Lecture II
• Convex mirror
• Image is always
(virtual, upright), smaller.
11
Lenses
• Convex lens bulges out –
converges light
• Concave lens caves in –
diverges light
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12
Focus
• Light goes through – focal points on
both sides – F and F’
– Always a question which focal point to
choose when ray tracing
• Converging lens:
– Parallel beam of light is converged in 1
point – focal point F
– Real focus: f>0
– Key for the focal point choice: Rays must
bend in
• Diverging lens:
– Parallel beam of light seems to be coming
out of 1 point F
– Virtual focus: f<0
– Key for the focal point choice: Rays must
bend out
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13
Ray tracing for converging lens
3 Easy rays:
1. Parallel  through
focus F
2. Through focus F’
parallel (reversible
rays)
3. Through the center 
itself
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Diverging lens
•
•
•
•
Same rules, but remember to diverge (bend out)
Parallel  projection through focus F
Projection through F’  parallel
Through the center  goes through
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Lens equation
1 1 1
 
do di
f
• d0 – distance to object
• di – distance to image
• f –focus
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1
P
f
• P – power of lens, in
Dioptry (D=1/m)
• f must be in m
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16
Sign convention for lenses and
mirrors
d0>0
h0>0
di>0 – real image
Opposite side from O
hi>0 – upright image
f>0 – concave mirror
f>0 – converging lens
hi
di
m

ho
do
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di<0 - virtual image
Same side with O
hi<0 - inverted image
f<0 – convex mirror
f<0 – diverging lens
•hi>0di<0 – upright image is always virtual
•hi<0di>0 – inverted image is always real
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17
Images in lenses and mirrors
• Converging lens, concave
• Diverging lens, convex
mirror
mirror
• d0>2f – (real, inverted), smaller
• Image is always
• 2f>d0>f – (real, inverted),
larger
(virtual, upright), smaller.
• d0<f – (virtual, upright), larger
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System of lenses
• Image of the 1st lens of object for the 2nd lens.
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Eye as an optical instrument
• Eye is a converging lens
• Ciliary muscles are used to
adjust the focal distance.
– f is variable
• Image is projected on
retina – back plane.
– di stays constant
• Image is real (light excites
the nerve endings on
retina)  inverted (we see
things upside-down)
– di>0, hi<0
• Optic nerves send ~30
images per second to brain
for analysis.
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20
Far and near points for normal eye
• Relaxed normal eye is focused on objects at infinity – far point
f0=eye diameter =~2.0 cm
• Near point – the closest distance at which the eye can focus - for
normal eye is ~25cm. Adjusted focus:
f1=1.85 cm
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21
Corrective lenses
• Nearsighted eye
– far point<infinity
– diverging lens f<0  P<0
• Farsighted eye
– near point > 25 cm
– converging lens f>0  P>0
• Lens+eye = system of lenses
• Corrective lenses create virtual, upright image (di<0 !) at the
point where the eye can comfortably see
• Nearsighted eye
• Farsighted eye
Far point = 17 cm  di =-0.17m Near point = 70 cm  di =-0.70m
Need to correct near point
Need to correct far point
Object at “normal near point”
Object at “normal far point”
d

0
.
25
m
=25cm
o
d


=infinity
o
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22
Images in lenses
• Converging lens - for
• Diverging lens - for
farsighted
nearsighted
• d0>2f – (real, inverted), smaller
• Image is always
• 2f>d0>f – (real, inverted),
(virtual, upright),
larger
smaller.
• d0<f – (virtual, upright), larger
Image in corrective lenses is always virtual and upright
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Lecture II
di<0 and hi>0
23
Corrective lenses
• Nearsighted eye
Far point = 17cm
Near point = 12 cm
P-?
new near point -?
Diverging lens projects infinity
to 17 cm from the eye
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24
Real and virtual image
Mirrors:
I and O –
same side
I and O –
opposite sides
Lenses:
I and O –
opposite sides
I and O –
same side
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Real, inverted
O
I
light goes through
M
Virtual, upright
O
M
I
light does not go through
Real, inverted
O
L
I
light goes through
Virtual, upright
O
I
L
Lecture II
light does not go through
25