LECTURE 14
LENSES
Instructor: Kazumi Tolich
Lecture 14
2
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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
Demo 1
5
¨
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
6
¨
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
7
¨
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
8
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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 through 4
Demo: 2
10
¨
Image Formation
¤ Demonstration
of a double convex lens forming an inverted and diminished
or enlarged image.
./
n
./
n
n 𝑑$
+
.0
+
23./
=
=
1
1
= , where 𝐷 is the distance between the light source and the screen.
2± 26 3721
9
¤ Demonstration
of the image of a half-covered lens.
Example: 1 (Walker Ch. 26-71)
11
¨
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
12
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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)
13
¨
Two lenses that are 𝐷 = 35 cm apart
are used to form an image. Lens 1 is
converging and has a focal length
𝑓- = 14 cm; lens 2 is diverging and
has a focal length 𝑓9 = -7.0 cm. The
object is placed 𝑑$,- =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
14