Hong Kong Polytechnic University Light Control through Optical System
Our major concerns: field of view and image brightness
We will learn: aperture, stop, aperture stop, field stop, pupil and window.
The element in an optical system that determines the maximum cone of
light passing through the system is called the aperture stop (AS).
The limiting cone angle 1 is easy to obtain but 2 is not.
Optics 1----by Dr.H.Huang, Department of Applied Physics
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Hong Kong Polytechnic University Light Control through Optical System
A front stop serves as an aperture stop.
Entrance pupil (EnP): the image of AS seen through the optical elements in
front of it.
Exit pupil (ExP): the image of AS formed by all imaging elements following it.
EnP is conjugate with ExP.
Optics 1----by Dr.H.Huang, Department of Applied Physics
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Hong Kong Polytechnic University Light Control through Optical System
A rear stop behind the lens
serves as the aperture stop
(AS) and the exit pupil (ExP).
A front stop serves as the
aperture stop (AS) and the
entrance pupil (EnP).
Optics 1----by Dr.H.Huang, Department of Applied Physics
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Hong Kong Polytechnic University Light Control through Optical System
Chief ray: a ray from object that passes through the axial point in EnP. The
ray must also passes through the axial point of both the AS and ExP.
Entrance and exit pupils are related to AS and govern the brightness of the
image.
Optics 1----by Dr.H.Huang, Department of Applied Physics
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Hong Kong Polytechnic University Light Control through Optical System
The field of view describes the range of the object
that can be viewed.
The partial shielding of the outer portion of the
image by stop S for off-axis object points is called
vignetting. Excessive vignetting may make the
image of a point object appear astigmatic.
The field of view (object plane) is often defined as
the circle (OU) that consisting of all object points
having at least half the maximum irradiance found at
the center of the image.
Field stop (FS) limits the size or angular width of the
object that can be imaged.
Entrance window (EnW): the image of FS formed by
all optical elements preceding it.
Exit window (ExW): the image of FS
formed by all optical elements following
it.
Optics 1----by Dr.H.Huang, Department of Applied Physics
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Hong Kong Polytechnic University Light Control through Optical System
Example: Consider an optical system made up of two positive thin lenses with a stop S
located between them as shown in the figure. (a) Locate the position and size of the final
image. (b) Locate the AS, EnP, and ExP for the system. (c) Locate the FS, EnW, and ExW for
the system.
1 1 1
 
s1=20 cm;
s1 s1 f1
1 1
1
 
m2 
s2=20 cm;
s2 s2 f 2
Solution: s1=40 cm; f1=40/3 cm;
s2=10 cm; f2=20/3 cm;
s1
1
m1   
s1
2
s2
 2
s2
Optics 1----by Dr.H.Huang, Department of Applied Physics
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Hong Kong Polytechnic University Light Control through Optical System
(b) Lens L1 is AS and EnP. Using thin lens equation, ExP is located 8.57 cm to the right of
lens L2 with an diameter of 4/7 cm.
(c) To find FS, we must determine the angles subtended at the center of the entrance pupil.
The stop S is FS. EnW is located in the
object plane with a diameter of 2 cm.
ExW is located at the image plane with
a diameter of 2 cm.
A schematic eye:
Optics 1----by Dr.H.Huang, Department of Applied Physics
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Hong Kong Polytechnic University Light Control through Optical System
Homework:
1. Two positive lenses, each of diameter 5 cm and focal length 15 cm, are separated by a
distance of 10 cm. For what range of object positions along the optical axis will (a) the
first lens and (b) the second lens control the amount of light passing through the system?
2. An aperture of opening 5 cm in diameter is positioned 15 cm to the left of a positive lens
of rim diameter 10 cm and focal length 12 cm. Each element is centered on the optical
axis. (a) For an object located 6 cm to the left of the aperture, which element serves as
AS? (b) Where are the entrance and exit pupils located?
3. An aperture of 5-cm opening is located 8 cm to the right of a positive lens of diameter 10
cm and focal length 12 cm. (a) For an object located 6 cm to the left of the lens, which
element is AS? (b) Where is EnP? What is its size? (c) Where is ExP? What is its size?
4. An object measures 2 cm high above the axis of an optical system of a 2-cm AS and a thin
convex lens of 5-cm focal length and 5-cm aperture. The object is 10 cm and the AS is 2
cm in front of the lens. Determine the position and size of the entrance and exit pupils, as
well as the image.
5. An optical system, centered on an optical axis, consists of (left to right): object plane, thin
lens L1 30 cm from the object plane, aperture A 15 cm farther from L1, thin lens L2 10 cm
farther from A, and image plane. Lens L1 has a focal length of 10 cm and a diameter 6
cm; L2 has a focal length of 5 cm and a diameter of 6 cm; aperture A has a centered,
circular opening of 2.0 cm in diameter. Locate (a) image plane, (b) AS and EnP, (c) ExP
and (d) FS, EnW and ExW.
Optics 1----by Dr.H.Huang, Department of Applied Physics
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Hong Kong Polytechnic University
Optical Instrumentation
Prisms: generally not used alone
Angular deviation:
A  1   2
  1   2  1  2  1  2
 A   min 
sin 

Minimum deviation occurs when
2


n

the ray of light passes through the
A
sin
prism symmetrically.
2
For small prism angle: n 
Or:
 min  An 1
 A   min  2
A2
Ophthalmic Prisms: Small angle prisms are used in
ophthalmology to correct double vision. When two eyes
do not aim simultaneously at an object correctly, tow
nonoverlapping images are perceived.
Optics 1----by Dr.H.Huang, Department of Applied Physics
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Hong Kong Polytechnic University
Optical Instrumentation
Bending power of prism (prism diopter pd):
measured in terms of the displacement y caused
by the prism on a screen 1 m from the prism.
Pprism  100 tan   100
Pprism  100n  1
For two thin prisms:
P  1001   2   P1  P2
Example: An ophthalmic prism of prism power Pprism=2.5 is desired. If the prism material
is of index n=1.56, what should be its apex angle? How should it be oriented to bend the ray
downward from the horizontal?
Solution:

Pprism
100n  1
 0.0446
The apex angle should be about 2.6 with base downward.
Optics 1----by Dr.H.Huang, Department of Applied Physics
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Hong Kong Polytechnic University
Optical Instrumentation
Example: A prism material has an index of 1.50 and apex angle of 5. (a) What is the
power of the prism? (b) By how much does it displace an incident ray at 60 cm?
Solution: Pprism  100n  1  4.36 pd
The ray is displaced 4.36 cm at a distance of 100cm. So it is displaced 2.6 cm at 60 cm.
Example: Two small angle prisms, both base down, are used in combination. One has a
power of 2.5 pd, the other of 4.4 pd. (a) What is the deviation angle of the pair? (b) What is
the displacement at 100 cm from the pair?
Solution: Pprism  P1  P2  6.9

Pprism
 0.069 rad  3.95
100
The displacement is 6.9 cm at 100 cm and is downward toward the base of the
prism.
Dispersion: angular spread
Cauchy equation:
n  A
B

2

C

4
 ...
Optics 1----by Dr.H.Huang, Department of Applied Physics
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Hong Kong Polytechnic University
Optical Instrumentation
Three specified colors are used:
· C line (656.3 nm) from a hydrogen vapor lamp.
· d line (587.2 nm) from a sodium lamp.
· F line (486.1 nm) from a hydrogen vapor lamp.
The refractive indices of substances for these
three precise colors are denoted by nC, nd, and nF,
respectively.
D
 mean

D
 F   C nF  1  nC  1 nF  nC


nD  1
D
nD  1
Dispersive power:   nF  nC
nD  1
An instrument using a prism as a dispersive
element, which is able to measure the angles of
deviation of various wavelength, is called a prism
spectrometer.
Optics 1----by Dr.H.Huang, Department of Applied Physics
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Hong Kong Polytechnic University
Optical Instrumentation
Prisms may be combined to produce achromatic overall behavior, that is, the net
dispersion D for two given wavelength may be made zero, even though the
deviation is not zero.
The direct vision prism accomplishes zero deviation for a particular wavelength
while at the same time providing some dispersion.
achromatic prism
For particular wavelength:
P1  P2
D1  D2
Optics 1----by Dr.H.Huang, Department of Applied Physics
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Hong Kong Polytechnic University
Optical Instrumentation
Camera:
It forms a real, inverted image on a
light sensitive surface by a converging
lens.
Below is a Zeiss Tessar system
produces a flat, well-focused image
over a large angular field.
f-number (relative aperture), exposure E;
exposure time Δt; and intensity I.
f /#  f D
E  It
I
1
 f /# 2
E
t
 f /# 2
If the f-number is 8, it is usually referred
to f/8 by photographers.
Optics 1----by Dr.H.Huang, Department of Applied Physics
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Hong Kong Polytechnic University
Optical Instrumentation
Depth of Focus
The blur disc diameters PQ and RS are their maximum, above which blur
would be noticed in an image in the planes PQ or RS. The distance between
the blur discs is known as the depth of focus for the image B. It is increased
with a smaller aperture.
Optics 1----by Dr.H.Huang, Department of Applied Physics
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Hong Kong Polytechnic University
Optical Instrumentation
Depth of Field
l1
l'2
l
l'
l'1
l2
l1  l l1  d
D
l   l2  l2  d D
2l 2 d
B2 B1  l1  l2 
l D
+
1 1 1 1
  
l1 l1 l  l
1 1 1 1
  
l2 l2 l  l
l1 
=
l
l d

l D
l
l2 
l d

l D
Optics 1----by Dr.H.Huang, Department of Applied Physics
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Hong Kong Polytechnic University
Optical Instrumentation
Example: A camera with a 5-cm focal length lens and f/16 aperture is focused on an
object 274.3 cm away. Allowing satisfactory quality of the image when d is 0.04 mm, what
are the near and far distances and the depth of field?
Solution: d=0.04 mm, f/D=16, f=5 cm, D=5/16 cm, l=274.3 cm,
l
1
1
l



 162 cm
near point: 1

l
d
1 d 1 1 d 1 1 


   
l D
l D l  l D  l f 
l
1
1
far point: l2 


 883 cm
l d
1 d 1 1 d 1 1 


   
l D
l D l  l D  l f 
The depth of field is 721 cm.
Optics 1----by Dr.H.Huang, Department of Applied Physics
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Hong Kong Polytechnic University
Optical Instrumentation
Angular Magnification
The visual angle  is aided with the lens and  is the unaided angle.
M
 tan 
h
h
 hq



 tan  d  l   q hd  l 
 Lq
Lq
M

Ld  1 L 1  dL
The angular magnification is dependent on the position of the observer’s eye
(distance d).
Optics 1----by Dr.H.Huang, Department of Applied Physics
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Hong Kong Polytechnic University
Optical Instrumentation
Nominal Magnification
When the image is formed at infinity,
M is referred to as the nominal
magnification Mnom. And is equal of
one-quarter of the lens power.
M nom 
F
4
M max  1 
F
4
Eyepieces:
The eyepieces, or ocular, of an instrument is fundamentally a magnifier. Its function
is to view the image (called objective) formed by a lens or lens system preceding it
in an optical instrument. Most types of eyepieces consist essentially of two lenses
referred to respectively as the field lens (it increases the field of view) and the eye
lens (is placed next to the observer’s eye).
Optics 1----by Dr.H.Huang, Department of Applied Physics
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Hong Kong Polytechnic University
Optical Instrumentation
Huygens Eyepiece:
The two lenses are separated by a
distance equal to the average of
their focal lengths.
The function of the field lens is to
deviate inward those rays which
would otherwise have missed the
eye lens, thus increasing the field
of view.
Huygens eyepiece reduces
longitudinal chromatic aberration.
Optics 1----by Dr.H.Huang, Department of Applied Physics
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Hong Kong Polytechnic University
Optical Instrumentation
Ramsden Eyepiece
Ramsden eyepiece consists of
two same plano-convex lenses,
separated by about 2/3f. The
final image is formed at infinity.
The function of the field lens is
to deviate towards the axis
those
rays
which
would
otherwise miss the eye lens.
This increases the field of view.
Optics 1----by Dr.H.Huang, Department of Applied Physics
21
Hong Kong Polytechnic University
Optical Instrumentation
Microscope
The
simplest
form
of
microscope consists of two
positive powered lenses: the
objective (O-lens) which has a
shorter focal length and the
eyepiece (-lens) which has a
longer focal length.
In normal use the final image is
at the standard near point
distance of 25cm from the lens.
Optics 1----by Dr.H.Huang, Department of Applied Physics
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Hong Kong Polytechnic University
Optical Instrumentation
Microscope
If the observer’s eye is emmetropic and unaccommodated, the final image must
be formed at infinity instead of at the standard near point. This is achieved by
withdrawing the -lens slightly such that the primary image falls on the first focal
plane of this lens. More prolonged viewing of the image is possible with less eye
strain.
Optics 1----by Dr.H.Huang, Department of Applied Physics
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Hong Kong Polytechnic University
Telescope
Optical Instrumentation
The telescope is used to enlarge
the image of a distant object.
The figure shows the image
formation
by
a
Keplerian
Astronomical Telescope.
In
normal usage the primary image
also coincides with the first focal
plane of the eyepiece.
The equivalent power of the afocal
configuration telescope is zero.
The instrument enlarges the visual
angle.
Optics 1----by Dr.H.Huang, Department of Applied Physics
24
Hong Kong Polytechnic University
Optical Instrumentation
Telescope
The terrestrial telescope
with an erector lens. With
the erector lens, the
telescope is longer but the
image viewed is upright.
The Galilean telescope
with a diverging eyepiece.
The final image is upright.
Optics 1----by Dr.H.Huang, Department of Applied Physics
25
Hong Kong Polytechnic University
Optical Instrumentation
Homework:
1. A parallel beam of white light is refracted by a 60 glass prism in a position of minimum
deviation. What is the angular separation of emerging red (n=1.525) and blue (n=1.535)
light?
2. Ophthalmic prisms of 2.0 and 3.0 pd are to be designed for the left and right lenses,
respectively, of a pair of eyeglasses, in order to correct for a 5.0 pd misalignment in the
vertical vision of a patient. The prism in the left lens is to produce a downward
displacement of the light passing through it, while the prism in the right lens is to produce
an upward displacement. The glass used for each lens has a refractive index of 1.523. (a)
What is the prism apex angle for each ophthalmic prism? (b) What is the orientation of
the prism base in each lens?
3. A prism of 60 refracting angle gives the following angles of minimum deviation when
measured on a spectrometer: C line, 3820; D line, 3833; F line, 3912. Determine the
dispersive power of the prism.
4. A camera is used to photograph three rows of students at a distance 6 m away, focusing on
the middle row. Suppose that the image defocusing or blur circles due to object points in
the first and third rows is to be kept smaller than a typical silver grain of the emulsion, say
1 m. At what object distance nearer and farther than the middle row does an
unacceptable blur occur if the camera has a focal length of 50 mm and a fnumber of f/4?
Optics 1----by Dr.H.Huang, Department of Applied Physics
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