Transcript PHY 231 Lecture 29 (Fall 2006)

Physics 213
General Physics
Lecture 16
Last Meeting: Reflection and
Refraction of Light
Today: Mirrors and Lenses
t
1
Are the red and violet lights coming
from the same raindrop?
2
Dispersion by drops of water. Red is bent the least so comes
from droplets higher in the sky.
Why is the sky blue?
Why is the sunset orange?
hint
4
Why is the
cloud white?
5
6
7
8
9
∞
10
demo
11
12
13
14
Funny Mirror
15
16
17
18
19
20
21
22
23
24
25
Ray Diagram for Diverging Lens


The image is virtual
The image is upright
26
QUICK QUIZ 23.4
A plastic sandwich bag filled with water
can act as a crude converging lens in
air. If the bag is filled with air and
placed under water, is the effective lens
(a) converging or (b) diverging?
QUICK QUIZ 23.4 ANSWER
(b). In this case, the index of refraction of
the lens material is less than that of the
surrounding medium. Under these
conditions, a biconvex lens will be
divergent.
Between F’ and O
F’
O
F
Image
Behind lens,
virtual, upright
larger than object
Example
Magnifying glass
At F’
Between
F’ and 2F’
2F’
F’
F’
O
O
F
F
At 2F’
2F’
F’
O
F
Beyond 2F’
2F’
F’
O
F
At infinity
2F’
F
F’
O
No image
Beyond 2F,
real, inverted,
larger
At 2F, real,
inverted,
same as object
Lighthouse
Projector
Office copier
Between F and 2F,
Real, inverted, smaller
Camera
At F, real, inverted,
smaller
Camera
Example: (a) An object 31.5 cm in front of a certain lens is imaged
8.20 cm in front of that lens (on the same side as the object). What
type of lens is this and what is its focal length? Is the image real or
virtual? (b) If the image were located, instead, 38.0 cm in front of the
lens, what type of lens would it be and what focal length would it
have?
Solution: (a) 1/do+1/di=1/f where do=31.5 cm, di=-8.20 cm
1/31.5+1/(-8.20)=1/f, which yields f=-11.1 cm, thus
diverging lens. The image is in front of the lens, so it is virtual
(b) Similarly, we have 1/31.5+1/(-38.0)=1/f. which gives
f=+184 cm, thus, converging lens.
(a)
F
Image
(b)
F’
F’
O
F
Question: An object infinitely far from a
converging lens has an image that is
(a) real
(b) virtual
(c) upright
(d) larger than the object
Answer: a
31
Question: An object farther from a
converging lens than its focal point
always has an image that is
(a) inverted
(b) virtual
(c) the same in size
(d) smaller in size
Answer: a
32
Quiz: An object closer to a converging lens
than its focal point always has an image
that is
(a) inverted
(b) virtual
(c) the same in size
(d) smaller in size
Answer: b
33
Sign Conventions for Mirrors
Concave gives “+” conventions
1 1 2
 
p q R
h'
q

h
p
1 1 1
 
p q f
M 
Sign Conventions for Refracting
Surfaces/Lenes
These are the same sign conventions – so just remember them for thin lenses.
n1 is the source medium
n2 is the observing medium
n1 n2 n2  n1


p q
R
n1q
h'
M

h
n2 p
h'
q

h
p
1 1 1
 
p q f
M 
1
1
1 
 (n  1) 


f
R
R
 1
2 
Combinations of Thin Lenses






The image produced by the first lens is calculated as though the second lens
were not present
The light then approaches the second lens as if it had come from the image of
the first 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
If the image formed by the first lens lies on the back side of the second lens,
then the image is treated at a virtual object for the second lens
 p will be negative
The overall magnification is the product of the magnification of the separate
lenses