Transcript Cardinal planes/points in paraxial optics

Optical systems:
Magnifier, microscope,
telescope & binoculars
Hecht 5.7
Wednesday October 9, 2002
1
Hand Magnifier
With thin lens What is the angular magnification of the
image for an object at the near point or at ∞?
H,H’
h”
θ’
F
hM’
so
f
s’
L
l
2
Compound Microscope
x’
L
Fe
Fo
Fo
Fe
Recall xx’ = fo2
x
Wish to have intermediate image (h’)
just inside the focus of the eyepiece
s’ ≈ fo + L
s = x + fo
L  fo
h'
s'
Mo     
h
s
x  fo
x’ ≈ L
x = fo2/L
L
Mo  
fo
3
Compound Microscope
L
Fe
h
Fo
Fo
h’
Fe
h”
Recall: The magnification of an image formed
(a) at the near point is
(b)at infinity
Me 
Me 
25cm
fe
25cm
1
fe
4
Compound microscope
Total magnification
L
M  M oM e  
fo
M  M oM e  
L
fo
 25cm 


 fe 
 25cm


 1
 fe

(Image at infinity)
(Image at near point)
5
Compound Microscope
In most microscopes, L ~ 16 - 17 cm
Objective
Mo  
Eyepiece
L
fo
10 X, 20 X, 40 X etc
10X 
L
 10 f o  1.7cm
fo
25cm (image at ∞)
Me 
fe
fe = 2.5 cm
Me = 10
40X  fo = 0.4 cm
Overall magnification M = 40X10 = 400
6
Compound Microscope
L
A.S.
Fe
Fo
Fo
Fe
EnP
ExP
Where should the eye be located to view the image?
Optimum viewing –
Place eye near ExP (moving eye away decreases illumination and F.O.V.)
Ensure that exit pupil ~ same size as eye pupil!
7
Compound Microscope
L
A.S.
Fe
Fo
Fo
Fe
EnP
ExP
Chief Ray
Marginal ray
8
Numerical Aperture
Measure of light gathering power
N. A. = n sin α
Lens
Air
Oil
αo
α g’ α g
αa
ng
Cover Glass
O
9
Numerical Aperture
If cover glass in air
N. A.  ng sin  g  1sin  a
If cover glass immersed in oil (no = 1.516) – between glass
and oil there is essentially no refraction since ng = 1.5
N. A.  ng sin  g '  no sin o  1.5 sin o
Increases the light gathering power by about 1.5
(N.A. roughly analogous to f# of a lens)
10
Numerical Aperture
In optical fibres
Cladding
θ
no
αmax
n2
θc
Core n1
Cladding
n2
2
n
2
2
N.A. = nosinαmax= n1sin θ = n1sin (90o - θc) = n1cos θc  n1 1  22  n1  n2
n1
This is a measure of the maximum cone of light accepted
11
Viewing distant objects, e.g. stars
star
θ
h
feye
Image size on retina h = feyeθ
12
Telescope
Objective
Eyepiece
fo
fe
θ’
θ
hT=feyeθ’
h’
θ’
h”
s’
13
Telescope
Show
fo
M 
fe
Dexit
Do

M
(magnification of the telescope)
(diameter of the exit pupil)
14
The Hubble Space Telescope
0.3 m secondary
mirror
2.4 m primary
mirror
15
Binoculars
Two telescopes side-by-side
Prisms used to erect images
Objective
Eyepiece
16
Binoculars
“6 X 30”
Angular Magnification (M)
Dexit 
Diameter of objective lens, Do (mm)
Do
M
Exit pupil = 5 mm, a good match to the normal pupil diameter
For night viewing, a rating of 7 X 50 is better: i.e. ~ 7 mm
17