Transcript Chapter 13: Mirrors and Lenses

Chapter 13: Mirrors and Lenses
• Section 1 : Mirrors
• Section 2: Lenses
• Section 3: Optical Instruments
Section 1 : Mirrors
Plane mirrors
• A mirror with a flat, smooth surface
 Your reflection in a plane mirror is what another person
would see if he/she looked at you
• How the mirror works:
 Light rays travel from the
source to you
 Every point struck by the
light reflects the waves so
that they travel outward in
all directions
 The reflected rays strike the
mirror and are reflect back to
you
• Virtual images
 Remember, your brain always interprets light rays as if
they have traveled in a straight line
 Doesn’t recognize if the rays are reflected or refracted
 If the reflected rays were extended behind the mirror they
would meet at a single point
 Your brain thinks that the rays that enter your eyes are
coming from this point, and seem to see your reflection at
this point (your reflections seems to come from behind
the mirror)
 The reflected image is a virtual image
 Light rays diverge and do not pass through you
Section 1 : Mirrors
Concave mirrors
• The surface of the mirror curves inward
• Principal axis (aka optical axis) - an imaginary line drawn
perpendicular to the surface of the mirror at its center
• Focal point – point on the principal axis through which the
reflected rays of rays drawn parallel to the principal axis pass
 If a light ray passes through the focal point and then
strikes the mirror, the reflected ray will be parallel to the
principal axis
• Center of curvature – an imaginary point on the principal axis
that marks the center of the circle that would be formed if
the ends of the mirror were extended.
 If a light ray passes through the center of curvature, the
reflected ray will pass through the focal point
• Focal distance – the distance from the center of the mirror to
the focal point is the
object
image
C
F
F = focal point; C = center of curvature
principal
axis
Section 1 : Mirrors
Concave mirrors
The location of an object relative to the focal point (F) and the
center of curvature (C) determines the type of image that will
be formed by the light reflected from the mirror:
1. Object infinite distance from a concave mirror - reflected
rays all pass through the focal point, and no image is formed
2. Object a finite distance beyond center of curvature - image
formed is real, inverted, reduced, and located between C
and F
3. Object located on center of curvature - image formed is real,
inverted, same size as the object, and located at C
4. Object between C and F - image is real, inverted, enlarged,
and located behind C
5. Object is on the focal point - rays are reflected parallel to
each other, no image is formed
6. Object is between F and the mirror - image is virtual,
upright, enlarged, and located behind the mirror
Section 1 : Mirrors
Convex mirrors
• The surface of the mirror curves outward
image
F
C
principal
axis
 The image formed is virtual, upright, reduced, and located
behind the mirror between the mirror and the focal point
Section 2: Lenses
A lens is a transparent material with at least one curved surface
the causes light rays to refract as they pass through
• There are two types of lenses
 Concave – a lens that is thicker
at the edges than in the center
 Convex – a lens that is thicker in
the center than at the edges
Section 2: Lenses
The image formed by light passing through a convex lens is
relative the location of the object when referenced by two
points located on the principal axis located at 1 focal length (F)
and two focal lengths (2F)
object
2F’
F’
F
2F
image
1. Object an infinite direction from lens - The rays are parallel to
the principal axis and the image formed is a point at the real
focus
2. Object at a finite distance beyond 2F’ - Image is real,
inverted, reduced and located between F and 2F
3. Object at a distance equal to 2F’ - Image is real, inverted, the
same size as the object, and located at 2F
4. Object at a distance between F’ and 2F’ - Image is real,
inverted, enlarged, and located beyond 2F
5. Object is at a distance of F’ - The rays are parallel to each
other as they leave the lens no image is formed
6. Object at a distance between F’ and the lens - Image is
virtual, upright, enlarged, and located between 2F’ and F’
Section 2: Lenses
Concave lens
• Also called a divergent lens because light rays diverge as
they pass through the lens
object
F’
F
image
 The only image formed is virtual, upright, reduced, and
located between F’ and the lens
Section 2: Lenses
Lenses and eyesight
• The structure of the eye gives you the ability to focus on
objects around you
 In a normal eye, light
travels through the
cornea to the convex
shaped lens
 The waves converge
on the focal point on
the retina where they
are converted into electrical impulses and sent to the
brain via the optic nerve
 In order to focus on objects, the lens in your eyes must be
flexible so the focal length changes
 Muscles control the shape of the lens
 When focusing on distant objects, the muscles stretch
the lens making it less convex and increasing the focal
length
 When focusing on close objects, the muscles make the
lens more convex and so decreasing the focal length
 Your eyes lose this focusing ability when you are
around 50 years old
Section 2: Lenses
Vision problems
• Farsightedness – can see distant objects
clearly but cannot focus on nearby objects
 Eyeball is too short, the focal point is
behind the retina – a convex
(converging lens) lens will correct
this problem
• Nearsightedness – can see close objects
clearly, but cannot focus on distant
objects
 Eyeball is too long, the focal point
is in front of the retina – a concave
(diverging) lens will correct this
problem
• Astigmatism – the surface of the cornea is curved unevenly
 Causes blurry vision at all distances
 Corrective lenses will be curved to cancel this unevenness
Calculations for Mirrors and Lenses
The lens/mirror equation
• There is a relationship between the focal length or the lens
or mirror and the object and image distances
The equation:
1
1
1
=
+
f
do
di
Where: f = focal length
do = object distance
di = image distance
Example: What is the focal length or the object is 10-cm from
the lens and the image formed is 12-cm?
1
1
1
Solution d = 10 cm
=
+
o
di = 12 cm
f=?
f
do
di
1
1
1
=
f
10cm 12 cm
1
= 0.1833
f
1
f=
0.1833
f = 5.45 cm
• You can also solve for do and di
1
1
1
=
+
f
do
di
1 1
1
1
1
=
+
f di
do
di di
1
1 1
= do
f di
1
1
1
=
+
f
do
di
1 1
1
1
1
=
+
f do
do
di do
1
1 1
= di
f do
Calculations for Mirrors and Lenses
Magnification
• Magnification is the ratio of the size (height) of the image to
the size (height) of the object, or:
M=
hi
ho
Where: M = magnification
hi = image height
ho = object height
Example: If the object is 56-cm high, and the image formed is
20-cm, what is the magnification?
Solution
ho = 5.0 cm
hi = 20.0 cm
M=?
hi
ho
20 cm
M=
5 cm
M=4
M=
Notice that the distance units cancel, magnification is just a
number.
Calculations for Mirrors and Lenses
Size/distance Equation
• As you saw with the ray diagrams, the size and location of the
image changes depending on the size and location of the
object
• There is an equation expressing the relationship between
object size and distance and image size and distance
Si
di Where: Si = image size
=
So = object size
So
do
di = image distance
do = object distance
• If you know any of the three variables you can solve for the
fourth
 By cross-multiplying , the equation goes from:
𝑆𝑖
𝑆𝑜
=
𝑑𝑖
𝑑𝑜
to this: 𝑆𝑖 𝑑𝑜 = 𝑆𝑜 𝑑𝑖
 Once the equation is in this form you can solve for
any variable
Example: A 10-cm object, 12-cm from a lens, forms an 8cm image. How far from the lens is the image?
Solution
So = 10 cm
Si
di
do = 12 cm
Si = 8 cm
di = ?
=
So
do
S id o
S o di
=
So
So
S id o
di =
So
8 cm(12 cm )
10 cm
96 cm
di =
10
di = 9.6 cm
di =