Physics 102: Lecture 17, Slide 1 Physics 102: Lecture 17 Reflection and Refraction of Light
Physics 102: Lecture 17, Slide 1
Physics 102: Lecture 17
Reflection and Refraction of Light
Physics 102: Lecture 17, Slide 2
Recall from last time….
Reflection:
Refraction:
Flat Mirror: image equidistant behind
Spherical Mirrors:Concave or Convex
Tod
ay
La
st T
ime θi θr
θ1
θ2
n2
n1
θi = θr
n1 sin(θ1)= n2 sin(θ2)
Physics 102: Lecture 17, Slide 3
O
Concave Mirror Principal Rays
fc
1) Parallel to principal axis reflects through f.
#1
3) Through center.
#3
Image is (in this case):• Real (light rays actually cross)• Inverted (Arrow points opposite direction)• Reduced (smaller than object)
**Every other ray from object tip which hits mirror will reflect through image tip
2) Through f, reflects parallel to principal axis.
#2
I
Physics 102: Lecture 17, Slide 4
C f1)
2)
3)
p.a.
Preflight 17.1
Ray through center should reflect back on self.
20%
45%
35%
Which ray is NOT correct?
Physics 102: Lecture 17, Slide 5
O
I
Mirror Equation
1do
+1di
=1f
fc
do
di
• 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 +R/2
• Negative: convex mirror –R/2
Works for concave,convex, or flat
Physics 102: Lecture 17, Slide 6
Preflight 17.3The image produced by a concave mirror of a real
object is:
1) Always Real
2) Always Virtual
3) Sometimes Real, Sometimes Virtual
Physics 102: Lecture 17, Slide 7
ACT: Concave MirrorWhere in front of a concave mirror should you
place an object so that the image is virtual?
1) Close to mirror
2) Far from mirror
3) Either close or far
4) Not Possible
Physics 102: Lecture 17, Slide 8
• •
• •
• •
3 Cases for Concave Mirrors
Inside FC FObject Image
C FObject
Image
C FObject
Image
Between C&F
Past C
Real
Virtual
Real
Physics 102: Lecture 17, Slide 9
O
I
Magnification Equationdo
do
ho
Angle of incidence
di
-hi Angle of reflection
o
i
o
i
dd
hhm −=≡
o
o
dh
=)tan(θi
i
dh−
=
di
• ho = height of object:• Positive: always
• hi = height of image:• Positive: image is upright
• Negative: image is inverted
• m = magnification:• Positive / Negative: same as for hi
• < 1: image is reduced
• > 1: image is enlarged
θθ
θ
θ
Physics 102: Lecture 17, Slide 10
Solving EquationsA candle is placed 6 cm in front of a concave mirror with
focal length f=2 cm. Determine the image location.
cm 211
cm 61
=+id
di = + 3 cm (in front of mirror)
Real Image!
C fp.a.
Preflight 17.2Compared to the candle, the image will be:
• Larger
• Smaller
• Same Size
Physics 102: Lecture 17, Slide 11
ACT: MagnificationA 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
2) 4 inches
3) 8 inches
What direction will the image arrow point?
1) Up 2) Down
4 inches
Physics 102: Lecture 17, Slide 12
• •
• •
• •
3 Cases for Concave Mirrors
Inside FC FObject Image
C FObject
Image
C FObject
Image
Between C&F
Past C
Inverted
Enlarged
Real
Upright
Enlarged
Virtual
Inverted
Reduced
Real
Physics 102: Lecture 17, Slide 13
f
image object
Demo: • two identical spherical mirrors• each mirror is positioned at the focal point of the other
Demo: optical illusion
Physics 102: Lecture 17, Slide 14
O
Convex Mirror Rays
c
1) Parallel to principal axis reflects through f.
2) Through f, reflects parallel to principal axis.
#2 I
3) Through center.
#3
Image is:Virtual (light rays don’t really cross)Upright (same direction as object)Reduced (smaller than object)
(always true for convex mirrors!):
f
#1
Physics 102: Lecture 17, Slide 15
Solving EquationsA candle is placed 6 cm in front of a convex mirror with focal length f=-3 cm. Determine the image location.
Determine the magnification of the candle.
If the candle is 9 cm tall, how tall does the image candle appear to be?
Physics 102: Lecture 17, Slide 16
Preflight 17.4The image produced by a convex mirror of a
real object is
1) always real
2) always virtual
3) sometimes real and sometimes virtual
Physics 102: Lecture 17, Slide 17
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•
•
1do
+1di
=1f
o
i
o
i
dd
hh
m −=≡
Physics 102: Lecture 17, Slide 18
Index of Refraction
Frequency is the same,wavelength decreases
Recall speed of light c = 3x108 m/s is in vacuumIn a medium (air, water, glass...) light is slower
n is a property of the medium:nvacuum = 1nair = 1.0003nwater = 1.33nglass = 1.50
v = c/nn ≥ 1
c = λ/f
v < ccλ1 λ2
Speed of light in vacuum
Speed of light in medium
“Index of refraction”
vacuum glass
Physics 102: Lecture 17, Slide 19
Reflected wave
Refracted wave
Incident wave
n1
n2 > n1λ2 < λ1
λ1
θ1 θr
θ2
Snell’s law of Refraction
n1 sin(θ1)= n2 sin(θ2)
When light travels from one medium to another, v (and λ) changes (v = c/n). So the light bends!
Physics 102: Lecture 17, Slide 20
n1
n2
Snell’s Law Practice
n1 sin θ1 = n2 sin θ2
no
rma
l
2θ
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 θr = 60. The other part of the beam is refracted. What is θ2?
sin(60) = 1.33 sin(θ2)
θ2 = 40.6 degrees
θ1 = θr = 60
θ1 θr
Usually, there is both reflection and refraction!
Physics 102: Lecture 17, Slide 21
n2
n1
d
d′
′ d = d n2
n1
Apparent depth:
Apparent Depth
50
actual fish
apparent fish