Download 13.1 to 13.4 Lenses and Lens Equations

I think it’s an ancient eye exam
Lens: ______________________________________________________.
 There are plane, concave and convex sides so the lens is classified by
the effect on the image
Converging Lens: ___________________________
 1 or 2 convex sides
 The centre is thicker then the ends
Diverging Lens: __________________________
 1 or 2 concave sides
 The centre is thinner then the edges
Converging Lens
Axis of Symmetry
Light rays parallel to the
principal axis pass through the
lens and converge at the focal
point on the opposite side.
Principle Axis
2F'
Secondary Focal Point (F')
(F')
0
O: centre of the lens called the optical centre
* To tell the (F and F') apart, the focus on
the opposite side of the lens as the
incident rays or object is called the (F)
2F
Focal Point (F)
There are two focal points
on a lens because light can
pass though either side
The size of the lens and shape of the curve affect the focal length
Diverging Lens
Axis of Symmetry
Light rays that are parallel to
the principal axis, do not
converge but spread out on the
other side. If we project these
diverging rays backward, it
looks like they come from a
virtual focus called the focal
point.
Principle Axis
0
2F
Focal Point (F)
2F'
Secondary Focal Point
(F')
O: centre of the lens called the optical centre
* To tell the (F and F') apart, the focus on
the same side of the lens as the
incident rays or object is called the (F)
There are two focal points
on a lens because light can
pass though either side
Rules for Drawing Ray Diagrams for Lenses (Laws of Refraction)
 All rays that enter a lens parallel to the principal axis (refract) leave
through the focal point (F)
 All rays that enter a lens appearing to come from the secondary focal
point leave the lens (refract) parallel to the principal axis
 All rays that pass through O (the optical centre) are not refracted and
pass through the lens at the same angle
Converging Lenses
1. Draw a principal axis and a vertical line through the centre of lens
(the axis of symmetry)
2. Mark and label the focal points (F) and (F')on both sides of the lens
3. Draw the object so it sits on the principal axis
4. Draw an incident ray from the top of the object to the lens parallel to
the principal axis. As the ray passes through the lens the line refracts
(bends) to go through the focal point on the other side.
5. Draw an incident ray from the top of the object to the lens through
the focal point on the same side. As the ray passes through the lens
the line refracts (bends) to be parallel to the principal axis.
6. Draw an incident ray from the top of the object to the lens through
the optical centre, it is not refracted.
7. Find the point where the rays meet and draw the image. The bottom
of the image is on the principal axis
Example 1: Object beyond 2F'
S:
A:
L:
T:
Example 2: Object at 2F'
S:
A:
L:
T:
Example 3: Object between F' and 2F'
S:
A:
L:
T:
Example 4: Object at F'
S:
A:
L:
T:
Example : Object between F' and O
S:
A:
L:
T:
Summary of image properties of Converging lenses
OBJECT
Location
Beyond 2F'
At 2F'
Between 2F'
and F'
At F'
Inside F'
Size
smaller
Attitude
inverted
Same size
Larger
Inverted
Inverted
No clear image
Larger
Upright
IMAGE
Location
Between 2F
and F
At 2F
Beyond 2F
Larger
(behind lens)
Type
Real
Real
Real
virtual
Diverging Lenses
1.
Draw a principal axis and a vertical line through the centre of lens (the
axis of symmetry)
2.
Mark and label the focal points (F) and (F')on both sides of the lens
3.
Draw the object so it sits on the principal axis
4.
Draw an incident ray from the top of the object to the lens parallel to the
principal axis. As the ray passes through the lens the line refracts
(bends) and travels in line as if it were originating from the focal point on
the same side.
5.
Draw an incident ray from the top of the object traveling towards the
secondary focal point on the opposite side. As the ray passes through the
lens the line refracts and will be parallel to the principal
6.
Draw an incident ray from the top of the object to the lens through the
optical centre, it is not refracted.
7.
Find the point where the rays meet and draw the image. The bottom of
the image is on the principal axis
8.
Example 9.
6: Image in a diverging lens -all object locations
10.
Any incident ray traveling parallel to the principal axis of a diverging lens
will refract through the lens and travel in line with the focal point (i.e., in a
direction such that its extension will pass through the focal point).
11.
Any incident ray traveling towards the focal point on the way to the lens will
refract through the lens and travel parallel to the principal axis.
S: smaller
12.
An incident ray that passes through the center of the lens will in affect
continue in the same direction that it had when it entered the lens.
A:upright
L: same side
as object
T: virtual
There are two ways to determine the characteristics of images formed by lenses:
1. Using ray diagrams (what we have done)
2. Using algebra (math)
Lens Terminology:
do: distance from the object to the optical centre
di: distance from the image to the optical centre
ho: height of the object
hi: height of the image
f: focal length of the lens: distance from the optical centre to the focal point
F. (notice the focal length is the same whether it goes from F or F')
2F
2F’
,
Thin lens equation
1 + 1 = 1
do
di
f
To use this equation you need to follow the sign convention
 Object distances (do) are always positive for real images (when the image is n the
opposite side of the lens as the object) and negative for virtual images (when the
image is on the same side of the lens as the object)
 The focal length (f) is positive for converging lenses and negative for diverging
lenses.
Ex. A converging lens has a focal length of 17cm. A candle is located 48 cm from the
lens. What type of image will be formed and where will it be located?
The Magnification Equation
When you compare the size of an image to the size of the object you are determining the
magnification of the lens.
M = hi = -di
ho do
Two new sign conventions need to be added in addition to the ones above to use this
equation.
 Object (ho) and image (hi) heights are positive when measured upward from the
principal axis and negative when measured downward.
 Magnification (M) is positive for an upright image and negative for an inverted
image.
Ex. A toy of height 8.4cm is balanced in front of a converging lens. An inverted, real
image of height 23cm is noticed on the other side of the lens. What is the magnification
of the lens?
Human Eye
 The cornea refracts the light before it enters the eye
 The retina responds to light and initiates nerve impulses
 The lens changes shape to refract light so we are able to focus light
from both near by and distant objects
Myopia (near-sightedness)
 The eyes cannot focus on distant objects
 The eyeball is too long and the image forms in front of the retina
Hyperopia (far-sightedness)
 The eyes cannot focus on nearby objects
 The eyeball is too short and the image if formed behind the retina
Laser Eye Surgery: A laser is used to change the cornea, which results in
improved vision. Side effects include dry eyes, oversensitivity to light, poor
perception of contrast, double vision and perception of ghosted images.