# 36.3 Images Formed by Refraction - PowerPoint PPT Presentation

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## 36.3 Images Formed by Refraction

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### Images by Refraction, 3 ... Real images are formed by refraction in the back of the surface ... Images from lenses. Light passing through a lens experiences ... – PowerPoint PPT presentation

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Title: 36.3 Images Formed by Refraction

1
36.3 Images Formed by Refraction
2
Images Formed by Refraction
• Consider two transparent media having indices of
refraction n1 and n2
• The boundary between the two media is a spherical
• Rays originate from the object at point O in the
medium with n n1

3
Images by Refraction, 2
• We will consider the paraxial rays leaving O
• All such rays are refracted at the spherical
surface and focus at the image point, I
• The relationship between object and image
distances can be given by
• (36.8)

4
Images by Refraction, 3
• The side of the surface in which the light rays
originate is defined as the front side
• The other side is called the back side
• Real images are formed by refraction in the back
of the surface
• Because of this, the refraction sign conventions
for q and R are opposite the reflection sign
conventions

5
Sign Conventions for Refracting Surfaces
6
Flat Refracting Surfaces
• If a refracting surface is flat, then R ??,
therefore
• q ?(n2 / n1)p (36.9)
• The image formed by a flat refracting surface is
on the same side of the surface as the object
• For n1 n2 a virtual image is formed between the
object and the surface
• For n1 of the object

7
Active Figure 36.20
(SLIDESHOW MODE ONLY)
8
Example 36.5 Gaze Into the Crystal Ball
• A set of coins is embedded in a spherical plastic
paper weight of radius 3.0 cm, with n 1.50. One
coin is located 2.0 cm from the edge of the
sphere. Find the position of the image of the
coin.
• Here n1 n2 so a virtual image is formed inside
the paperweight.
• R is negative

9
36.4 Thin Lenses
• Lenses are commonly used to form images by
refraction
• Lenses are used in optical instruments
• Cameras, telescopes, microscopes
• Images from lenses
• Light passing through a lens experiences
refraction at two surfaces
• The image formed by one refracting surface serves
as the object for the second surface

10
Image Formed by a Lens
• The lens has an index of refraction n and two
spherical surfaces with radii of R1 and R2
• R1 is the radius of curvature of the lens surface
that the light of the object reaches first
• R2 is the radius of curvature of the other
surface
• The object is placed at point O at a distance of
p1 in front of the first surface

11
Image From Surface 1
• There is an image formed by surface 1
• Since the lens is surrounded by the air, n1 1
and n2 n ?
• Equation (36.8) becomes
• (36.10)
• If the image due to surface 1 is virtual, q1 is
negative, and it is positive if the image is real

12
Image From Surface 2
• For surface 2, n1 n and n2 1
• The light rays approaching surface 2 are in the
lens and are refracted into air
• Use p2 for the object distance for surface 2 and
q2 for the image distance, so equation (36.8)
becomes
• (36.11)
• From the virtual image at surface 1 p2 q1
t
• q1 is negative and t is the thickness of the lens
• From the real image at surface 1 p2 q1
t
• q1 is positive

13
Image Formed by a Thin Lens
• A thin lens is one whose thickness t is small
compared to the radii of curvature
• For a thin lens, the thickness, t, of the lens
can be neglected
• In this case, p2 q1 for either type of image
• Hence equation (36.11) becomes
• (36.12)

14
Image Formed by a Thin Lens, 2
• Adding equations (36.10) and (36.12) we obtain
• (36.13)
• Then the subscripts on p1 and q2 can be omitted
as in the figure and rewrite equation (36.13) as
• (36.14)

15
Lens Makers Equation
• The focal length f of a thin lens is the image
distance q that corresponds to an infinite object
distance
• This is the same as for a mirror
• Making p ? ? and q ? f, so equation (36.14) will
become the lens makers equation
• (36.15)
• Given n and f the lens maker can determine the
values of R1 and R2
• Given R1, R2 and n lens maker can calculate the
value of f

16
Thin Lens Equation
• Using equation (36.15) we can write equation
(36.14) in a for identical to equation (36.6) for
mirrors.
• The relationship among the focal length, the
object distance and the image distance is the
same as for a mirror
• (36.16)

17
Notes on Focal Length and Focal Point of a Thin
Lens
• Because light can travel in either direction
through a lens, each lens has two focal points
• One focal point is for light passing in one
direction through the lens
• The other is for light traveling in the opposite
direction
• However, there is only one focal length
• Each focal point is located at the same distance
from the lens

18
Focal Length of a Converging Lens
• The parallel rays pass through the lens and
converge at the focal point
• The parallel rays can come from the left or right
of the lens

19
Focal Length of a Diverging Lens
• The parallel rays diverge after passing through
the diverging lens
• The focal point is the point where the rays
appear to have originated

20
Determining Signs for Thin Lenses
• The front side of the thin lens is the side of
the incident light
• The back side of the lens is where the light is
refracted into
• This is also valid for a refracting surface

21
Sign Conventions for Thin Lenses
22
Magnification of Images Through a Thin Lens
• The lateral magnification of the image is
• When M is positive, the image is upright and on
the same side of the lens as the object
• When M is negative, the image is inverted and on
the side of the lens opposite the object

23
Thin Lens Shapes
• These are examples of converging lenses
• They have positive focal lengths
• They are thickest in the middle

24
More Thin Lens Shapes
• These are examples of diverging lenses
• They have negative focal lengths
• They are thickest at the edges

25
Ray Diagrams for Thin Lenses Converging
• Ray diagrams are convenient for locating the
images formed by thin lenses or systems of lenses
• For a converging lens, the following three rays
are drawn
• Ray 1 is drawn parallel to the principal axis and
then passes through the focal point on the back
side of the lens
• Ray 2 is drawn through the center of the lens and
continues in a straight line
• Ray 3 is drawn through the focal point on the
front of the lens (or as if coming from the focal
point if p
parallel to the principal axis

26
Ray Diagram for Converging Lens, p f
• The image is real
• The image is inverted
• The image is on the back side of the lens

27
Ray Diagram for Converging Lens, p
• The image is virtual
• The image is upright
• The image is larger than the object
• The image is on the front side of the lens

• 28
Ray Diagrams for Thin Lenses Diverging
• For a diverging lens, the following three rays
are drawn
• Ray 1 is drawn parallel to the principal axis and
emerges directed away from the focal point on the
front side of the lens
• Ray 2 is drawn through the center of the lens and
continues in a straight line
• Ray 3 is drawn in the direction toward the focal
point on the back side of the lens and emerges
from the lens parallel to the principal axis

29
Ray Diagram for Diverging Lens
• The image is virtual
• The image is upright
• The image is smaller
• The image is on the front side of the lens

30
Active Figure 36.28
(SLIDESHOW MODE ONLY)
31
Image Summary
• For a converging lens, when the object distance
is greater than the focal length
• (p )
• The image is real and inverted
• For a converging lens, when the object is between
the focal point and the lens, (p
• The image is virtual and upright
• For a diverging lens, the image is always virtual
and upright
• This is regardless of where the object is placed

32
Fresnal Lens
• Refraction occurs only at the surfaces of the
lens
• A Fresnal lens is designed to take advantage of
this fact
• It produces a powerful lens without great
thickness

33
Fresnal Lens, cont.
• Only the surface curvature is important in the
refracting qualities of the lens
• The material in the middle of the Fresnal lens is
removed
• Because the edges of the curved segments cause
some distortion, Fresnal lenses are usually used
only in situations where image quality is less
important than reduction of weight

34
Two Thin Lenses (Combination)
• If two thin lenses are used to form an image
• The image formed by the first lens is located as
if the second lens were not present
• Then a ray diagram is drawn for the second lens
• The image of the first lens is treated as the
object of the second lens
• The image formed by the second lens is the final
image of the system

35
Two Thin Lenses, 2
• If the image formed by the first lens lies on the
back side of the second lens, then the image is
treated as a virtual object for the second lens
• p will be negative
• The same procedure can be extended to a system of
three or more lenses
• The overall magnification is the product of the
magnification of the separate lenses

36
Two Thin Lenses, 3
• Consider a case of two lenses in contact with
each other
• The lenses have focal lengths of 1 and 2
• If p1 p is the object distance for the
combination, equation (36.16) becomes
• Since the lenses are in contact, p2 q1

37
Two Thin Lenses, final
• For the second lens q2 q ,
• Adding the two previous equations for the
combination of the two lenses
• (36.17)
• Two thin lenses in contact with each other are
equivalent to a single thin lens having a focal
length given by the above equation

38
Example 36.6 Where is the Final Image?
39
Example 36.6 Where is the Final Image? , 2
• The location of the image formed by lens 1
• The image of lens 1 becomes object for lens 2,
with p2 20cm 15cm 5cm ?
• Then, the total magnification will be

40
Material for the Midterm