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QUESTIONS? PLEASE ASK!
Review
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Single slit diffraction

In general, destructive
interference occurs for a single slit
of width for:
l
sinq dark = m
a
m = 1, 2, 3, …
Polarization
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Natural light is unpolarized
Polarization occurs through selective
absorption, reflection, scattering
Polarization through absorption
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Transmission through crossed
polarizers: Malus’s Law
IT = Io cos2 θ

Polarization by reflection

Brewster’s angle
n = tan θp
Chapter 25
http://static-p4.fotolia.com/
Optical Instruments
http://www.misericordia.mb.ca/Programs/ecAnatomy.html
Camera
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Converging lens
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Image is formed on an electric
device
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CCD, CMOS
Shutter – exposure time
Aperture – light intensity
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Produces a real image
Light intensity I ~ D2/f2
ƒ-number - ratio of lens focal
length to diameter

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ƒ-number = f/D
ƒ-number  lens “speed”

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A lens with a low f-number is a
“fast” (and expensive) lens
Camera lenses typcially range
from 1.4 -11
The Eye
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Amazing optical instrument!
The normal eye focuses
light and produces a sharp
image
Essential parts of the eye
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The pupil
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A variable aperture
The crystalline lens
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Cornea – light passes
through this transparent
structure
Aqueous Humor – clear
liquid behind the cornea
Most of the refraction takes place at the outer surface of the eye
Iris (colored portion of the eye) muscular diaphragm that
controls pupil size

The f-number of the eye is from about 2.8 to 16
The Eye – Focusing

Accommodation

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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
focusing on a distant object
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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

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This is about 1.7 cm
Focusing on near objects
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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
The Eye – Near and Far Points
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near point - closest distance for which the lens
can accommodate to focus light on the retina
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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
far point - the largest distance for which the
lens of the relaxed eye can focus light on the
retina
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Normal vision has a far point of infinity
Farsightedness
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Also called hyperopia
The image focuses behind the retina
Can usually see far away objects
clearly, but not nearby objects
Correcting Farsightedness

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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
Nearsightedness
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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
Correcting Nearsightedness

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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
Problem 25.11 p 843
The
accommodation
limits
for
Nearsighted Nick’s eyes are 18 cm
and 80 cm. When he wears his
glasses, he can see far away objects
clearly. At what minimum distance
is he able to see objects clearly?
Diopters

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
P = 1/f
Simple Magnifier
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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
The Size of a Magnified Image
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When an object is
placed at the near
point, the angle
subtended is a
maximum

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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
Angular Magnification

Angular magnification is defined as
q
angle with lens
mº
=
qo angle without lens

The angular magnification is at a
maximum when the image formed by
the lens is at the near point of the eye

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q = - 25 cm
Calculated by
mmax
25 cm
= 1+
q
Problem 25.23 p 844
A leaf of length h is positioned 71 cm in front of a
converging lens with a focal length of 39 cm. An observer
views the image of the leaf at a position of 1.26 m behind
the lens.
(a) what is the magnitude of the lateral
magnification (the ratio of the image size to the object
size) produced by the lens? (b) What angular
magnification is achieved by viewing the image of the leaf
rather than viewing the leaf directly
Answer to 25.11
Answer to 25.23