Images from Mirrors and Lenses
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We have lots of book left to read in a little over a
month, and it's showing.
Depending on which version of the book you have, it
might not be as bad as it looks. We don’t do any
quantum mechanics, for example (Physics 222).
 Todays reading is long because lenses and mirrors are
very similar, so we will discuss their theory at the same
time. You will see applications of these principles during
lectures next week.
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Lots of questions about sign conventions.
What's the importance of real vs. virtual images?
Why are we worried about that?
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We’ll discuss this today.
Image from Wikipedia.
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An image is the appearance of an object where there really
isn’t one.
Real:
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Virtual:
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When the image is “real,” light rays pass through the image (or the
location of the image)
When the image is “virtual,” the light rays seem to come from the
image (but they don’t).
The distinction between “real” and “virtual” images doesn’t
refer to the position of the object.
“Real” and “Virtual” images can be inverted or not,
magnified or not.
You cannot tell from the image alone whether it is real or
virtual. (You need to also know where the object, mirrors,
and lenses are.)
Is the image you see
behind a flat mirror real
or virtual?
A. Real
B. Virtual
How can you ever get a real image to form with a mirror?
Concave mirrors can form real images
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Why do all paraxial rays hit the focal point?
Answer: This is true only for mirrors of a
special shape.
What shape is that?
Mirrors for which this is not true do not have a
well-defined focal point.
“Images” formed by these mirrors will appear
out-of-focus. (Abberation)
Why do rays passing through the focal point
get reflected parallel to the principle axis?
What is the focal length of a concave mirror with
a radius R?
A. R
B. -R
C. R/2
D. -R/2
E. R^2
Is the image real or virtual?
(Quick Quiz 36.3)
Consider the image in the mirror.
Based on the appearance of the
people, would you conclude that:
A. The mirror is concave and the
image is real?
B.
The mirror is concave and the
image is virtual?
C. The mirror is convex and the
image is real?
D. The mirror is convex and the
image is virtual?
Argh! This is hard!
focus
useful “third ray”:
center of mirror is flat
Where will an image appear that is placed in front
of a concave mirror at an approximate distance of
f/2?
p
ho
hi
focus
f
q
Similar triangles:
hi q

ho p
Similar triangles:
hi
f

hi  ho p
The equation:
1 1 1
 
p q f
p
ho
hi
focus
f
Similar triangles
hi q

ho p
hi
Define M: M 
ho
q
Useful way
q
to calculate: M  
Force M to be negative if image is inverted.
p
focus
focus
Ray diagram just like one for concave mirror, except
rays continue to right instead of reflecting back!
The equation:
1 1 1
 
p q f
positive q = right
hand side of lens
Magnification same:
q
M 
p
Assuming that the light rays are coming from the left:
quantity
positive
+
negative

p
if on the left of the
lens/mirror
if on the right of the lens/mirror
(can only happen in a
compound problem)
q
if on the right of the lens
(left side of mirror),
means a real image
if on the left of the lens
(right side of mirror),
means a virtual image
f
if converging: convex
lens/concave mirror
if diverging: concave
lens/convex mirror
M
if image is right-side up
if image is upside-down
Assuming that the light rays are coming from the left:
quantity
positive
+
negative

p
if on the left of the
lens/mirror
if on the right of the lens/mirror
(can only happen in a
compound problem)
q
if on the right of the lens
(left side of mirror),
means a real image
if on the left of the lens
(right side of mirror),
means a virtual image
f
if converging: convex
lens/concave mirror
if diverging: concave
lens/convex mirror
M
if image is right-side up
if image is upside-down
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Image of one becomes object of next
Worked problem: Find qfinal, Mtot
f = 20 cm
f = -60 cm
60 cm
15 cm
Answers: image is 20 cm to right of -60cm lens; M = -0.67