Revision problem
Chapter 18 problem 37 page 612
Suppose you point a pinhole camera at a 15m
tall tree that is 75m away….
1
Optical Instruments
•
Thin lens equation
•
Refractive power
•
Cameras
•
The human eye
•
Combining lenses
•
Resolution
2
Optical Instruments - continued
Optical imaging and color in
medicine
Integral part of diagnosis
3
Thin lens equation
Instead of using ray tracing, we can use
similar triangles to find the relationship
between f, s and s’
4
Thin lens equation
Magnification triangles:
h s
m

h
s
5
Thin lens equation
Focusing triangles:
h
s  f

h
f
6
Thin lens equation
Combining
h
s  f
s


h
f
s
1 s  f
1
1



s
sf
f
s
7
Thin lens equation
• Focal length, f
• Distance from object to lens, s
• Distance from image to lens, s’
1
1
1
 
f
s
s
8
Sign conventions
• Object distance, s
• is always positive for this course.
• Focal length, f
• is positive for converging lens, or concave mirror
• Is negative for diverging lens or convex mirror
• Magnification, M, and image height, h’
• are positive when image is upright
• are negative when image is inverted
9
Sign conventions
• Image distance s’
• Is positive for real images
• Is negative for virtual images
10
Sign Conventions for Lenses and Mirrors
11
Slide 19-11
Magnification
• Now use a sign convention, to indicate
whether image is upright (positive) or
inverted (negative)
h
s
M

h
s
12
Refractive power
A thicker lens will refract light at a larger angle and
have a shorter focal length, f.
We define the refractive power, P, as
1
P
f
Measured in diopters, 1D=1m-1
13
Refractive power of lenses in
contact
If two lenses are touching (or at least, very close),
their refractive powers add.
Useful for lenses which are close together – such as
corrective eye lenses
Ptotal  P1  P2
Measured in diopters, 1D=1m-1
14
Camera
• Simple single lens camera.
• Image is focused by a
convex lens
• Shutter used to allow the
light into the camera
• Recorded on CCD (used to
be photosensitive paper,
35mm in width)
15
Camera
CCD (Charge Coupled Device) is a 2D
array of 1to >20 million pixels – each of
which is a photosensitive semiconductor
with color filter
16
Camera
• Focusing achieved by
moving the lens
towards or away from
the image.
• Exposure is controlled
by changing the
diameter of an iris
behind the lens and the
shutter time
17
Camera exposure
• Exposure is related to
the amount of light
which is recorded.
• Controlled by shutter
speed and iris size
• Shutter speed is the
time the shutter is
open.
• Needs to be shorter for
fast moving images
18
Camera exposure
• Shutter speed is the
time the shutter is
open.
• Needs to be shorter for
fast moving images
• Expressed as fractions
of a second – 1/500s to
1/30s
19
Camera exposure
•Iris size controls the effective
diameter of the lens
•Measured as the f-number, the
ratio of the diameter of the lens, d,
and the focal length
f
f  number 
d
Focal length, f is fixed, and light intensity goes as
area, (d2 ), or 1/(f-number)2
Labeled as f-stops on a camera
20
Human Eye
• Focusing by the fixed
cornea, and the variable
lens
• Exposure controlled by
the iris
• Recorded by the retina
which contains
photosensitive cells
21
Human Eye Focusing
• The cornea acts as a
fixed lens.
• Corrections to the
focusing applied by
stretching the ciliary
muscles to curve the
lens, called
accommodation
22
Human Eye Focusing
• Far point – lens muscles relaxed – longest focal
length
• Near point – lens muscles fully contracted, shortest
focal length
23
Corrective lenses
Two common types of
conditions require corrective
lenses
• Myopia or near sightedness
rays converge in front of the
retina when the lens muscles
are relaxed
• Hyperopia or far sightedness
rays converge behind the
retina when the lens muscles
are relaxed
24
Correcting Myopia
Add a concave
lens to diverge
the light rays
(negative focal
length)
This increases
the far point
25
Correcting Hyperopia
Add a convex lens
Occurs when the eye is about 50 years old, and
the lens becomes less elastic, and cannot
curve.
26
Simple Magnifying lens
Increases the apparent size of an object.
Angular size for the magnified object is now
h
tan  

f
27
Simple Magnifying lens
h
 magnified 
f
h
• Compare the angular
 near 
25cm
size at near point and for
• Increases the apparent
size of an object.
the magnified object
• Magnifies up to 20
 magnified 25cm
M

 near
f
28
Compound Microscope
Simplest form contains two lenses
• Objective lens to create real image
• Eyepiece lens to magnify real image
29
Microscope
Magnification from the objective lens
s
L
M obj  

s
f obj
30
Microscope
Magnification from the eyepiece lens
M eye
25cm

f eye
31
Microscope
Total magnification is the product of the two
M total  M objM eye
L 25cm

f obj f eye
32
Telescope
Two stage magnification, but with weaker
objective lens
33
Telescope
We want the angular magnification
 eye
M
 obj
34
Telescope
Objective lens angle
h
 obj  
f obj
35
Telescope
Eyepiece lens angle
 eye
h

f eye
36
Telescope magnification
Total magnification
 eye
f obj
M

 obj
f eye
37
Reflecting Telescope
Need large aperture to capture more light –
large objective lens.
Easier to make a mirror than a lens, Newton
invented a reflecting telescope.
38
Resolution of optical instruments
Imperfections in the lens are called aberrations
Two main types
• Spherical aberration – poor focusing
• Chromatic aberration – color dispersion n(λ)
39
Correcting aberrations
• Spherical aberration – remove the edges of the
lens, using a smaller iris, but reduces image
intensity
• Chromatic aberration – use 2 lenses
40
Resolution from the wave model
• Telescopes, microscopes
and lenses all have
dimensions >> λ
• Images do not, however,
when the instruments are
used at their limits of
resolution
41
Resolution from the wave model
• To separate two circular
images, we would get 2
circular diffraction patterns
• Airy disk – with ring
fringes.
• The central disk has a
radius
  1.22

D
42
Telescope Resolution
• Called Rayleigh’s
criterion, relates the
angular resolution α,
wavelength, λ, and object
lens diameter
  1.22

D
43
Resolution of a Microscope
At the object end of a
microscope, the angular
separation, θmin, and
minimum resolvable
distance, dmin will be
 min
1.22

D
d min  f min
1.22f

D
44
Resolution of a Microscope
We replace D with 2f tanΦ,
which is nearly 2f sinΦ.
d min
0.61

sin 
45
Resolution of a Microscope
Some microscopes use a
transparent oil which
decreases the λ, and
decreases the minimum
resolution
d min
0.61o

n sin 
46
Resolving power of a Microscope
The resolving power of a microscope is defined by
d min
0.61o
 RP 
NA
Where NA is the numerical
aperture
NA  n sin 
47
Resolving power of a Microscope
Values of the numerical aperture are around 1 for an immersion
microscope, so the resolving power of a microscope can be as
small as 0.5λ, half the wavelength of light.
Smaller wavelengths can be obtained by using electron
microscopes, where the object is irradiated with beams of
electrons, to get from 2000x magnification to x1,000,000x
48
Summary
•
Thin lens equation
•
Refractive power
•
Cameras
•
The human eye
•
Combining lenses
•
Resolution
49