LECTURE 14
LENSES
Instructor: Kazumi Tolich
Lecture 14
2
¨
Reading chapter 26.6 - 26.7, and 27.2
¤ Ray
diagram for lenses
¤ Thin-lens equation
¤ Lenses in combination
Focal points
3
¨
¨
¨
¨
Lenses are used to focus light and form images.
Lenses have two focal points, one on each side.
Rays parallel to the axis converge at a focal point,
𝐹, on the refracted light side of a convex lens.
Rays parallel to the axis appear to originate from
a focal point, 𝐹, on the incident light side of a
concave lens.
𝐹
𝐹
Quiz: 1
4
¨
The index of refraction of the lenses are denoted by 𝑛#$%& , and that of the
medium in which the lens is placed is 𝑛'$()*' . Let 𝑘 = ./01 . Which
-2/3452
diagram correctly represents wave fronts passing through the lens placed in
the medium?
𝑘<1
𝑘>1
𝑘>1
𝑘=1
𝑘=1
Quiz: 14-1 answer
5
-./01
¨
If 𝑘 =
¨
lags where the lens is thicker.
If 𝑘 = 1, the light travels as fast in the lens as in the medium, so the wave
front does not bend.
-2/3452
𝑘<1
> 1, the light travels slower in the lens, so the wave front
𝑘>1
𝑘>1
𝑘=1
𝑘=1
Demo 1
6
¨
Fillable Air Lenses
¤ Air
filled convex lens in water is a diverging lens, opposite from a glass
convex lens in air being a converging lens.
Air convex lens in water
nwater > 1
nair = 1
Glass convex lens in air
nair = 1
nglass > 1
Ray diagrams
7
¨
The three principal rays for thin lenses are similar to those for mirrors:
¤
¤
¤
The parallel ray (P ray) approaches the lens parallel to its axis.
The focal ray (F ray) is drawn toward (concave) or through (convex) the focal point.
The midpoint ray (M ray) goes through the middle of the lens. Assuming the lens is thin
enough, it will not be deflected.
Thin-lens equation
8
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The thin-lens equation gives the relationship among the
focal length 𝑓, the object distance 𝑑; , and the image
distance 𝑑) .
1
1 1
+ =
𝑑; 𝑑) 𝑓
¨
The magnification, 𝑚, is defined to be
𝑚≡
ℎ)
𝑑)
=−
ℎ;
𝑑;
Sign conventions
9
¨
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Focal length, 𝑓:
¤
+ for converging (convex) lenses
¤
− for diverging (concave) lenses
Magnification, 𝑚:
¤
¤
¨
Image distance, 𝑑) :
¤
¤
¨
+ for upright image
− for inverted image
+ for opposite side of the lens from the object (real images)
− for same side of the lens as the object (virtual images)
Object distance, 𝑑; :
¤
¤
+ for real objects
− for virtual objects
Quiz: 2
¨
When a real object is placed just outside the focal point of a
diverging lens, what kind if image is formed? Choose all that
apply.
A.
B.
C.
D.
E.
F.
Diminished.
Enlarged.
Upright.
Inverted.
Real.
Virtual.
Quiz: 12-2 answer
¨
Diminished, Upright, Virtual.
¨
A
BC
¨
𝑚=−
B4
BC
𝑚 =
B4
BC
¨
¨
+
A
B4
A
D
= , where 𝑓 < 0. 𝑑) =
BC D
BC FD
< 0, so the image is virtual.
> 0, so the image is upright.
=
GC H
GC IH
BC
=
D
DFBC
< 1, so the image is diminished.
A diverging lens always create diminished, upright, and virtual images.
Quiz: 3
12
¨
A converging lens is used to project the image of an arrow onto a
screen. If the arrow is farther away from the lens than its focal length,
what kind of image is produced? Choose all that apply.
A.
B.
C.
D.
Real
Virtual
Upright
Inverted
Quiz: 14-3 answer
13
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Real and inverted
¨
A
BC
¨
𝑚=−
+
A
B4
A
D
= , where 0 < 𝑓 < 𝑑; . 𝑑) =
B4
BC
BC D
BC FD
< 0, so the image is inverted.
> 0, so the image is real.
Quiz: 4
14
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A piece of black tape is now placed over the upper half of the lens. Which of the
follow is true?
A.
B.
C.
Only the lower half of the object (i.e., the arrow tail) will show on the screen.
Only the upper half of the object (i.e., the arrow head) will show on the screen.
The whole object will still show on the screen.
Quiz: 14-4 answer
15
¨
¨
The whole object will still show on the screen.
The image will be dimmer because only half of the light now go
through the lens.
Demo: 2
16
¨
Image Formation
¤ Demonstration
of a double convex lens forming an inverted and diminished
or enlarged image.
A
BC
A
n
BC
n
n 𝑑;
+
A
B4
+
A
JFBC
=
=
A
D
A
D
= , where 𝐷 is the distance between the light source and the screen.
J± JM FNJD
P
¤ Demonstration
of the image of a half-covered lens.
Example: 1 (Walker Ch. 26-71)
17
¨
An object with a height of
ℎ; = 2.54 cm is placed
𝑑; = 36.3 mm to the left of
a lens with a focal length of
𝑓 = 35.0 mm.
A.
B.
Where is the image located?
What is the height of the
image?
Lenses in combination
18
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¨
In a two-lens system, the image produced by the first lens serves as
the object for the second lens.
The total magnification is the product of the magnifications of each
lens.
Example: 2 (Walker Ch. 26-66)
19
¨
Two lenses that are 𝐷 = 35 cm apart
are used to form an image. Lens 1 is
converging and has a focal length
𝑓A = 14 cm; lens 2 is diverging and
has a focal length 𝑓P = -7.0 cm. The
object is placed 𝑑;,A =24 cm to the
left of lens 1.
A.
B.
C.
Where is the location of the image?
Is the image upright or inverted?
Is the image real or virtual?
Quiz: 5
20
¨
A real image is formed by a converging lens. If a weak diverging lens is
placed between the converging lens and the image, where is the new image
located?
A.
B.
C.
farther from the converging lens than the original image
closer to the converging lens than the original image
at the original image position
Quiz: 14-5 answer
21
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¨
farther from the converging lens than the original image
The weak diverging lens diverges the rays slightly.