1
Physics 1230: Light and Color
Chuck Rogers, [email protected] Henley, Valyria McFarland, Peter Siegfried
physicscourses.colorado.edu/phys1230
Lecture 17:
Lenses and ray tracing
EXAM 2 is next week Thursday in-class
Online and Written_HW9 due TONIGHT
Last Time: Refraction all the way through block
What was happening in Activity 8?
U2L05 3
Convex and concave lenses
4
• Each of the two surfaces has a spherical shape.
• Light can penetrate through the lenses and bend at the air-lens interface.
Last Time: Concave and convex lenses
Glass
We build lenses out of glass with non-parallel sides
Which ray of light will have changed direction the most upon exiting the glass?
Glass
A
C
B
If slabs aren’t parallel - lens
7
We build lenses out of glass with non-parallel sides
Put film, Retina here!
8
• Light rays bent towards each other… CONVERGING LENS. • The less parallel the two sides, the more the light ray changes
direction.• Rays from a single point, converge to a single point on the other
side of the lens (and then start diverging again).
We build lenses out of glass with non-parallel sides
Put film, Retina here!
Focus
f
optical axis
Light rays coming in parallel focus to a point, called the focal point
Converging (convex) lens
10
a good light collector or solar oven; can also fry ants with sunlight (but
please don’t do that)
Light focusing properties of converging lens
11
The “backwards” light collector:create a collimated light beam
Light focusing properties of converging lens
12
n>1
Rays entering
“slower” material bend toward
normal
Rays entering
“faster” material bend away from
normal
n=1
Ray tracing:
1. As long as ray stays in
same medium, it goes
straight.
2. At each interface to a
different medium,
calculate how it will
bend. Go back to 1.
Ray tracing to understand lenses and images
This gets tedious!
13
FF
foci}focal lengthIf the glass surface is nearly a section of a
sphere, it will FOCUS
parallel rays.
A THIN LENS is very thin
compared to the focal
length. Then we can
simplify the treatment with
THREE SIMPLE RULES.
Thin convex (converging) lens
Group Activity!
• Come on down and get a handout.
• Your group should have a small focusing lens
• You should have a ruler or come get one.
• IT IS AN EXCELLENT IDEA TO HAVE A RULER FOR THE COMING EXAM 2.
Please get started on Part 1.
A Question:
You hold up a focusing lens and look through
it at an image of a distant object that is far on
the other side of the lens.
You find that the image is located at:
A)The object side of the lens
B)On your side of the lens
C)Exactly inside the lens
The image is:
A) Virtual B) Real
Group Activity!
Please get continue on Part II.
17
1) A ray parallel to the axis
is deflected through the
focus on the other side
2) A ray through the center
of the lens continues
undeviated
3) A ray coming from the
focus on one side goes
out parallel to the axis
on the other
F’F
1
2
3 3
foci
}focal lengthThin convex (converging) lens: Ray tracing rules
18
foci (focuses?)
Where will this ray go?
Ray tracing
19
Ray Tracing
Where will this ray go?
Suppose it’s emitted from this object
foci (focuses?)
Ray tracing
20
Ray Tracing
foci (focuses?)
We know where these 3 rays
go, using the simple ray rules
Ray tracing
21
Ray Tracing
foci (focuses?)
We know where these 3 rays
go, using the simple ray rules
Amazing property of
this lens: all rays from
the tip of the arrow will
converge to the same
point
Ray tracing
22
Amazing property of
this lens: all rays from
the tip of the arrow will
converge to the same
point (the image)
See how the rays emerge
from this point (the image)?
Ray tracing: Thin lens, object outside focus
23
Amazing property of
this lens: all rays from
the tip of the arrow will
converge to the same
point (the image)
Eye sees an image
here.The Lens acts as our
“Magic Ray Machine”, creating the rays to
produce an image.
Ray tracing: Thin lens, object outside focus
24
In this case, the image is:
Eye sees an image
here.
A)Virtual
B)Real
Clicker question
25
In this case, the image is:
Eye sees an image
here.
A)Virtual
B)Real
Real because the light rays really
go through the image. You can put
a screen there to see it.
Clicker question
Remember the Pinhole?
Pinhole = selecting one set of rays. Dim but always in focus!
Many pinholes = many images
Lens gathers and bends light from multiple rays to focus to one image
Demo and PHET Geometric-optics
http://phet.colorado.edu/en/simulation/geometric-optics
Idea of magnification and focused image
Group Activity!
Please get continue on Part II and
start to get to G.
29
Ray tracing a convex lens: object inside focus
30
Ray tracing a convex lens: object inside focus
The image appears larger (and farther away) than the object.
This is a magnifying glass.
(Remember: a magnifying glass is a convex lens.)
Aside: near-sighted people need concave/diverging lenses; can a marooned
myopic start a fire with his eye-glasses?
Converging/convex lens:Near objects are magnified and upright.Far objects are upside down and smaller
Near object
Far object
Magnifying glass
Group Activity!
Please get continue on Part 3.
Good place for a break!
Enjoy your day.
33
Ray tracing exercise
Ray tracing exercise
Come get some handouts!