This document discusses optical instruments such as cameras, the human eye, microscopes, telescopes, and their components and workings. It explains that cameras use lenses to focus light and form real images on film or digital sensors, and various components like the aperture and shutter control light intensity. The human eye focuses by changing the lens shape and has specialized cells on the retina for vision. Microscopes use two lenses to magnify small objects, and telescopes use lenses or mirrors to make distant objects appear larger.

1. Raymond A. Serway
Chris Vuille
Optical Instruments
1

2. Analysis generally involves the laws of reflection
and refraction.
Analysis uses the procedures of geometric optics
(Ray model of light).
However, To explain certain phenomena, the wave
nature of light must be used.
Introduction
2

3. The single-lens photographic camera is an optical
instrument.
Components
Opaque, light-tight box
Converging lens
Produces a real image
Film behind the lens
Receives the image
Section 25.1
3

4. Image is formed on an
electric device
 CCD – Charge-coupled
device
 CMOS – Complementary
metal-oxide semiconductor
Both convert the image
into digital form.
The image can be stored in
the camera’s memory.
Section 25.1
4

5. Proper focusing leads to sharp images.
The lens-to-film distance will depend on the object distance
and on the focal length of the lens.
The shutter is a mechanical device that is opened for
selected time intervals.
Most cameras have an aperture of adjustable diameter
to further control the intensity of the light reaching
the film.
With a small-diameter aperture, only light from the central
portion reaches the film, and spherical aberration is
minimized.
Section 25.1
5

6. Light intensity is a measure of the rate at which
energy is received by the film per unit area of the
image.
The intensity of the light reaching the film is
proportional to the area of the lens.
The brightness of the image formed on the film
depends on the light intensity.
Depends on both the focal length and the diameter of
the lens
Section 25.1
6

7. The ƒ-number of a camera is the ratio of the focal
length of the lens to its diameter.
ƒ-number = f/D
The ƒ-number is often given as a description of the lens
“speed”.
A lens with a low f-number is a “fast” lens.
Section 25.1
7

8. 8

9. Increasing the setting from one ƒ-number to the next
higher value decreases the area of the aperture by a
factor of 2.
The lowest ƒ-number setting on a camera corresponds
to the aperture wide open and the maximum possible
lens area in use.
Simple cameras usually have a fixed focal length and a
fixed aperture size, with an ƒ-number of about 11.
The high value of ƒ allows for a large depth-of-field.
Most cameras with variable ƒ-numbers adjust them
automatically.
Section 25.1
Example of
depth of
field 
9

10. 10

11. The normal eye focuses
light and produces a sharp
image.
Essential parts of the eye
 Cornea – light passes
through this transparent
structure
 Aqueous Humor – clear
liquid behind the cornea
Section 25.2
11

12. The pupil
A variable aperture
An opening in the iris
The crystalline lens
Most of the refraction takes place
at the outer surface of the eye.
Where the cornea is covered with
a film of tears
Section 25.2
12

13. The iris is the colored portion of the eye.
It is a muscular diaphragm that controls pupil size.
The iris regulates the amount of light entering the eye
by dilating the pupil in low light conditions and
contracting the pupil in high-light conditions.
The f-number of the eye is from about 2.8 to 16.
Section 25.2
13

14. The cornea-lens system focuses light onto the back
surface of the eye.
This back surface is called the retina.
The retina contains receptors called rods and cones.
These structures send impulses via the optic nerve to the
brain.
The brain converts these impulses into our conscious view of the
world.
Section 25.2
14

15. Rods and Cones
 Chemically adjust their sensitivity according to
the prevailing light conditions
 The adjustment takes about 15 minutes.
 This phenomena is “getting used to the dark”
Accommodation
 The eye focuses on an object by varying the
shape of the crystalline lens through this process.
 An important component is the ciliary muscle
which is situated in a circle around the rim of the
lens.
 Thin filaments, called zonules, run from this
muscle to the edge of the lens.
Section 25.2
15

16. The eye can focus on a
distant object.
The ciliary muscle is relaxed.
The zonules tighten.
This causes the lens to
flatten, increasing its focal
length.
For an object at infinity, the
focal length of the eye is
equal to the fixed distance
between lens and retina.
This is about 1.7 cm
Section 25.2
16

17. The eye can focus on near objects.
The ciliary muscles tense.
This relaxes the zonules.
The lens bulges a bit and the focal length decreases.
The image is focused on the retina.
Section 25.2
17

18. The near point is the closest distance for which
the lens can accommodate to focus light on
the retina.
Typically at age 10, this is about 18 cm.
Average is about 25 cm
It increases with age, to 500 cm or more at age 60.
The far point of the eye represents the largest
distance for which the lens of the relaxed eye
can focus light on the retina.
Normal vision has a far point of infinity.
Section 25.2
18

19. Eyes may suffer a mismatch between the focusing
power of the lens-cornea system and the length of
the eye.
Eyes may be
Farsighted
Light rays reach the retina before they converge to form an
image
Nearsighted
Person can focus on nearby objects but not those far away
Section 25.2
19

20. Also called hyperopia
The image focuses behind the retina.
Can usually see far away objects clearly, but not
nearby objects Section 25.2 20

21. A converging lens placed in front of the eye can correct
the condition.
The lens refracts the incoming rays more toward the
principle axis before entering the eye.
 This allows the rays to converge and focus on the retina.
Section 25.2 21

22. Also called myopia
In axial myopia the nearsightedness is caused by the lens
being too far from the retina.
In refractive myopia, the lens-cornea system is too
powerful for the normal length of the eye.
Section 25.2 22

23. A diverging lens can be used to correct the condition.
The lens refracts the rays away from the principle axis
before they enter the eye.
 This allows the rays to focus on the retina.
Section 25.2 23

24. Presbyopia is due to a reduction in
accommodation ability.
 The cornea and lens do not have
sufficient focusing power to bring
nearby objects into focus on the retina.
 Condition can be corrected with
converging lenses
In astigmatism, the light from a
point source produces a line image
on the retina.
 Produced when either the cornea or the
lens or both are not perfectly symmetric
 Can be corrected with lenses having
different curvatures in two mutually
perpendicular directions
Section 25.2
24

25. Optometrists and ophthalmologists usually prescribe
lenses measured in diopters.
The power of a lens in diopters equals the inverse of the
focal length in meters.

Section 25.2
25

26. A simple magnifier consists of a single converging
lens.
This device is used to increase the apparent size of an
object.
The size of an image formed on the retina depends on
the angle subtended by the eye.
Section 25.3
26

27. When an object is placed at the near point, the angle
subtended is a maximum.
 The near point is about 25 cm
When the object is placed near the focal point of a
converging lens, the lens forms a virtual, upright, and
enlarged image.
Section 25.3 27

28. Angular magnification is defined as
The angular magnification is at a maximum when
the image formed by the lens is at the near point
of the eye.
q = - 25 cm
Calculated by
Section 25.3
28

29. With a single lens, it is possible to achieve angular
magnification up to about 4 without serious
aberrations.
With multiple lenses, magnifications of up to about
20 can be achieved.
The multiple lenses can correct for aberrations.
Section 25.3
29

30. A compound microscope consists of two lenses.
 Gives greater magnification than a single lens
 The objective lens has a short focal length, ƒo<1 cm.
 The ocular lens (eyepiece) has a focal length, ƒe, of a few cm.
Section 25.4 30

31. The lenses are separated by a distance L.
L is much greater than either focal length.
The approach to analysis is the same as for any
two lenses in a row.
The image formed by the first lens becomes the object
for the second lens.
The image seen by the eye, I2, is virtual, inverted
and very much enlarged.
Section 25.4
31

32. The lateral magnification of the microscope is
The angular magnification of the eyepiece of the
microscope is
The overall magnification of the microscope is the
product of the individual magnifications
Section 25.4
32

33. The ability of an optical microscope to view an object
depends on the size of the object relative to the
wavelength of the light used to observe it.
For example, you could not observe an atom (d ≈ 0.1
nm) with visible light (λ≈ 500 nm).
Section 25.4
33

34. Two fundamental types of telescopes
Refracting telescope uses a combination of lenses to
form an image.
Reflecting telescope uses a curved mirror and a lens to
form an image.
Telescopes can be analyzed by considering them
to be two optical elements in a row.
The image of the first element becomes the object of
the second element.
Section 25.5
34

35. The two lenses are arranged so
that the objective forms a real,
inverted image of a distant
object.
The image is near the focal
point of the eyepiece.
The two lenses are separated
by the distance ƒo + ƒe which
corresponds to the length of
the tube.
The eyepiece forms an
enlarged, inverted image of the
first image.
Section 25.5 35

36. The angular magnification depends on the focal
lengths of the objective and eyepiece.
Angular magnification is particularly important
for observing nearby objects.
Very distant objects still appear as a small point of light.
Section 25.5
36

37. Large diameters are needed to study distant objects.
Large lenses are difficult and expensive to
manufacture.
The weight of large lenses leads to sagging which
produces aberrations.
Section 25.5
37

38. Helps overcome some of the disadvantages of
refracting telescopes
Replaces the objective lens with a mirror
The mirror is often parabolic to overcome spherical
aberrations.
In addition, the light never passes through glass.
Except the eyepiece
Reduced chromatic aberrations
Section 25.5
38

39. The incoming rays are
reflected from the mirror
and converge toward point
A.
 At A, a photographic plate or
other detector could be
placed.
A small flat mirror, M,
reflects the light toward an
opening in the side and
passes into an eyepiece.
Section 25.5
39

40. Reflecting Telescopes
Largest in the world are 10 m diameter Keck telescopes
on Mauna Kea in Hawaii
Largest single mirror in US is 5 m diameter instrument
on Mount Palomar in California
Refracting Telescopes
Largest in the world is Yerkes Observatory in Wisconsin
Has a 1 m diameter
Section 25.5
40

41. The ability of an optical system to distinguish
between closely spaced objects is limited due to
the wave nature of light.
If two sources of light are close together, they can
be treated as non-coherent sources.
Because of diffraction, the images consist of bright
central regions flanked by weaker bright and dark
rings.
Section 25.6
41

42. If the two sources are separated so that their
central maxima do not overlap, their images are
said to be resolved.
The limiting condition for resolution is Rayleigh’s
Criterion.
When the central maximum of one image falls on the
first minimum of another image, they images are said to
be just resolved.
The images are just resolved when their angular
separation satisfies Rayleigh’s criterion.
Section 25.6
42

43. If viewed through a slit of
width a, and applying
Rayleigh’s criterion, the
limiting angle of
resolution is
For the images to be
resolved, the angle
subtended by the two
sources at the slit must
be greater than θmin
Section 25.6
43

44. Section 25.6
44

45. The diffraction pattern of a circular aperture consists
of a central, circular bright region surrounded by
progressively fainter rings.
The limiting angle of resolution depends on the
diameter, D, of the aperture.
Section 25.6
45

46. If λ1 and λ2 are nearly equal wavelengths between
which the grating spectrometer can just barely
distinguish, the resolving power, R, of the grating
is
A grating with a high resolving power can
distinguish small differences in wavelength.
Section 25.6
46

47. The resolving power increases with order number.
R = Nm
N is the number of lines illuminated.
m is the order number.
All wavelengths are indistinguishable for the zeroth-
order maximum.
m = 0 so R = 0
Section 25.6
47

48. The Michelson Interferometer is an optical
instrument that has great scientific importance.
It splits a beam of light into two parts and then
recombines them to form an interference pattern.
It is used to make accurate length measurements.
Section 25.7
48

49. A beam of light provided by
a monochromatic source is
split into two rays by a
partially silvered mirror M.
One ray is reflected to M1
and the other transmitted
to M2.
After reflecting, the rays
combine to form an
interference pattern.
The glass plate ensures
both rays travel the same
distance through glass.
Section 25.7
49

50. The interference pattern for the two rays is determined by
the difference in their path lengths.
When M1 is moved a distance of λ/4, successive light and
dark fringes are formed.
This change in a fringe from light to dark is called fringe
shift.
The wavelength can be measured by counting the number
of fringe shifts for a measured displacement of M.
If the wavelength is accurately known, the mirror
displacement can be determined to within a fraction of the
wavelength.
Section 25.7
50

51. 51

52. 52

53. 53
(Continued)

54. 54