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Physics 102: Lecture 17
Reflection and Refraction of Light
Physics 102: Lecture 17, Slide 1
Exam 2 results
• Raw mean = 87.8 / 115 (76.3%)
• Scaled mean = 76.3%
– Raw mean improved by 10% compared to Exam 1
– Answers will be posted after March 18
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– Physics understanding?
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• Oh by the way...
– Next exam April 18
Physics 102: Lecture 17, Slide 2
Today
Last Time
Recall from last time….
Reflection:
qi = qr
qi qr
Flat Mirror:
image equidistant behind
Spherical Mirrors:
Concave or Convex
Refraction:
Physics 102: Lecture 17, Slide 3
n1 sin(q1)= n2 sin(q2)
q1
q2
n1
n2
Concave Mirror Principal Rays
1) Parallel to principal axis reflects through f.
2) Through f, reflects parallel to principal axis.
3) Through center.
O
#1
#2
#3
c
Image is (in this case):
• Real (light rays actually cross)
• Inverted (Arrow points opposite direction)
• Reduced (smaller than object)
Physics 102: Lecture 17, Slide 4
f
I
**Every other ray from object tip which hits
mirror will reflect through image tip
Preflight 17.1
Which ray is NOT correct?
Ray through center should reflect back on self.
p.a.
15% 1)
43% 2)
41% 3)
Physics 102: Lecture 17, Slide 5
C
f
Mirror Equation
1 1 1
 
do di f
do
Works for concave,
convex, or flat
• do = distance object is from mirror:
Positive: object in front of mirror
Negative: object behind mirror
• di = distance image is from mirror:
• Positive:
real image (in front of mirror)
• Negative: virtual image (behind mirror)
• f = focal length mirror:
• Positive:
concave mirror
• Negative: convex mirror
Physics 102: Lecture 17, Slide 6
+R/2
–R/2
O
f
c
I
di
Preflight 17.3
The image produced by a concave mirror of a real
object is:
46% 1) Always Real
16% 2) Always Virtual
38% 3) Sometimes Real, Sometimes Virtual
Concave mirror: f > 0
Real Object means in front of mirror: do > 0
Mirror Equation:
1 1 1
 
do di f

1
1 1
= di
f d0
di is positive if d0 > f; negative is d0 < f.
Physics 102: Lecture 17, Slide 7
ACT: Concave Mirror
Where in front of a concave mirror should you
place an object so that the image is virtual?
1) Close to mirror
Mirror Equation:
2) Far from mirror
3) Either close or far
4) Not Possible
• Concave mirror: f > 0
1 1 1
 
do di f
1 1 1
 
di f d 0
• Object in front of mirror: do > 0
• Virtual image means behind mirror: di < 0
• When do < f then di < 0 virtual image.
Physics 102: Lecture 17, Slide 8
3 Cases for Concave Mirrors
Virtual
C
•
•
F
Object
Image
Inside F
Real
Image
Object
C
•
C
•
Object
•
F
•
F
Image
Physics 102: Lecture 17, Slide 9
Between C&F
Past C
Real
Magnification Equation
do
hi
di
m 
ho
do
O
q
• ho = height of object:
• Positive:
q
always
• hi = height of image:
I
• Positive: image is upright
• Negative: image is inverted
• m = magnification:
• Positive / Negative: same as for hi
Angle of incidence
ho
q
• < 1: image is reduced
• > 1: image is enlarged
ho  hi
tan(q )  
-hi
d o di
Physics 102: Lecture 17, Slide 10
di
do
di
q
Angle of reflection
Solving Equations
A candle is placed 6 cm in front of a concave mirror with
focal length f=2 cm. Determine the image location.
1
1
1
 
6 cm di 2 cm
di = + 3 cm (in front of mirror)
Real Image!
Preflight 17.2
Compared to the candle, the
image will be:
p.a.
25% • Larger
66% • Smaller
9%
• Same Size
Physics 102: Lecture 17, Slide 11
C
f
ACT: Magnification
A 4 inch arrow pointing down is placed in front of a mirror
that creates an image with a magnification of –2.
What is the size of the image?
1) 2 inches
hi
m
ho
4 inches
2) 4 inches
3) 8 inches
Magnitude gives us
size.
hi  mh0  2 4
What direction will the image arrow point?
1) Up
2) Down (-) sign tells us it’s
inverted from object
Physics 102: Lecture 17, Slide 12
3 Cases for Concave Mirrors
Upright
C
•
•
F
Object
Image
Inside F
Enlarged
Virtual
Inverted
Image
C
•
Object
•
F
Between C&F
Enlarged
Real
Object
C
•
•
F
Image
Physics 102: Lecture 17, Slide 13
Past C
Inverted
Reduced
Real
Demo: optical illusion
f
image
object
Demo:
• two identical spherical mirrors
• each mirror is positioned at the focal point of the other
Physics 102: Lecture 17, Slide 14
Convex Mirror Rays
1) Parallel to principal axis reflects through f.
2) Through f, reflects parallel to principal axis.
3) Through center.
#1
O
#2
#3
I
f
Image is:
Virtual (light rays don’t really cross)
Upright (same direction as object)
Reduced (smaller than object)
(always true for convex mirrors!):
Physics 102: Lecture 17, Slide 15
c
Solving Equations
A candle is placed 6 cm in front of a convex mirror with
focal length f=-3 cm. Determine the image location.
1
1
1
 
6 cm di  3 cm
di = - 2 cm (behind mirror)
Virtual Image!
Determine the magnification of the candle.
di
- 2 cm
m

do
6 cm
m = + 1/3
If the candle is 9 cm tall, how tall does the image candle
appear to be?
hi
1/ 3 
9 cm
Physics 102: Lecture 17, Slide 16
hi = + 3 cm
Image is Upright!
Preflight 17.4
The image produced by a convex mirror of a
real object is
Mirror Equation:
1) always real
2) always virtual
1 1 1
 
do di f
3) sometimes real and sometimes virtual
• Convex mirror: f < 0
• Object in front of mirror: do > 0
• di < 0 means virtual image!
• Image is always between F
and mirror |di|<|f|
Physics 102: Lecture 17, Slide 17
1 1 1
 
di f d 0
di is
negative!
f is
negative
do is
positive
Mirror Summary
• Angle of incidence = Angle of Reflection
• Principal Rays
– Parallel to P.A.: Reflects through focus
– Through focus: Reflects parallel to P.A.
– Through center: Reflects back on self
• |f| = R/2
• 1 1 1
 
do di f
• m  hi   di
ho
Physics 102: Lecture 17, Slide 18
do
Index of Refraction
Recall speed of light c = 3x108 m/s is in vacuum
In a medium (air, water, glass...) light is slower
c
l1
l2
v<c
Frequency is the same,
wavelength decreases
v = lf
vacuum
glass
“Index of refraction”
Speed of light
in medium
Physics 102: Lecture 17, Slide 19
v = c/n
Speed of light
in vacuum
n is a property
of the medium:
nvacuum = 1
nair = 1.0003
nwater = 1.33
nglass = 1.50
n≥1
Snell’s law of Refraction
When light travels from one medium to another, v (and l)
changes (v = c/n). So the light bends!
n1 sin(q1)= n2 sin(q2)
Incident wave
Reflected wave
q1 q
r
l1
n2 > n 1
l2 < l1
Refracted wave
Physics 102: Lecture 17, Slide 20
n1
q2
Snell’s Law Practice
Usually, there is both reflection and refraction!
A ray of light traveling through the air (n=1) is incident on water
(n=1.33). Part of the beam is reflected at an angle qr = 60. The
other part of the beam is refracted. What is q2?
q1
qr
q2 = 40.6 degrees
n1
normal
n2
Physics 102: Lecture 17, Slide 21
q1 = qr = 60
sin(60) = 1.33 sin(q2)
n1 sin q1  n2 sin q2
q
2
Apparent Depth
Apparent depth:
n2
d  d
n1
n2
n1
d
apparent fish
d
actual fish
Physics 102: Lecture 17, Slide 22
See you after break!
Physics 102: Lecture 17, Slide 23