PHY138 – Waves, Lecture 9
Today’s overview
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Lenses
The Thin Lens Equation
Lenses Used in Combination
It’s the last week of the fall semester!
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The last Waves Problem Set is due at
5:00 PM today in your TA’s mailbox.
There is no Web-CT quiz until Jan.3.
There is a practice
www.masteringphysics.com assignment now
available (not due) on Chapter 26
material.
Announcements:
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Test 2 is at 9:00 AM sharp on Friday Dec.
10. You will need:
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A non-programmable calculator
An aid sheet with the main equations used
this quarter, and other info you think might
be useful. It may be double-sided, up to
8½×11” in size. It must be hand-written; no
shrink photocopies or condensed type!
Room Assignments are now listed on
the course web-site.
Quiz 1
air
water
A fish swims directly below the surface of
the water. An observer sees the fish at:
1. a greater depth than it really is.
2. its true depth.
3. a smaller depth than it really is.
Light going through a prism bends toward
the base
Building a Converging Lens out of Prisms
Snell’s Law of Refraction is obeyed at every
interface.
Converging Lens
Focal length, f
NOTE: Focal length is defined
for initially parallel rays.
Focal Point
Diverging Lens
Negative
Focal length, -f
Virtual Focal
Point
Rays appear to emerge
from Virtual Focal Point
Off-axis rays through a converging lens
NOTE: The ray which passes through the
centre of the lens is not bent.
Diverging rays through a Converging Lens
Focal length, f
This follows from the principle of reversibility.
Quiz 2
f
What will happen to the rays emerging to the
right of the lens if the face is moved a little
closer to the lens?
1. They will remain parallel.
2. They will diverge (spread out).
3. They will converge (toward a focus).
Quiz 3
f
What will happen to the rays emerging to the
right of the lens if the face is moved a little
further away from the lens?
1. They will remain parallel.
2. They will diverge (spread out).
3. They will converge (toward a focus).
Diverging rays through a Converging Lens
Focal length, f
q
p
1 1 1
 
p q f
Thin Lens Equation: sign conventions
image
object
f
p
1 1 1
 
p q f
q
p is positive for objects to the left of lens, negative
for objects to the right of lens (virtual objects).
q is positive for images to the right of lens, negative
for images to the left of lens (virtual images).
f is positive for converging lenses, negative for
diverging lenses.