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IVB. Geometric optics
2. Reflection
1. Wave front and rays
1 221
3. Refraction: Snell’s Law
2211 sinsin nn index of refraction:v
cn 1
221 ff 1
2
1
2
2
1
v
v
n
n
rays
wave fronts
Example:
12
23
n1 n2 n3
332211 sinsinsin nnn
1313 If nn
in out
normal to surface
diffuse reflection
23 fromt independen is n
1
Example:
?
50
33.1
00.1
2
1
2
1
n
n2211 sinsin nn
35
50sin33.1
00.1sinsin
2
12
12
n
n
2
4. Total internal reflection
1n 2
1
1
21
21
sin 0
900
n
nCC
21 nn 12 nn
2n
Example:
?
00.1
52.1
2
1
C
n
nn
1.41
52.1
11sin
1
2
C
C nn
n
2
1
3
900 12
1) Binoculars often use total internal reflection; this gives true 100% reflection, which even the best mirror cannot do.
4a. Applications of total internal reflection
2) Fiber optics.
The typical value of the index of refraction for optical fibers:•for the core n=1.48•for the cladding n=1.46
4
An image can be formed using multiple small fibers
Light will be transmitted along the fiber even if it is not straight
6.8048.1
46.1sin
1
2 CC n
n
5. Plane mirror
O I
dodi
O I
do di
Image in plane mirror:•virtual•erect•the same size
do = di
6. Comments about objects and images created by different optical instruments: curved mirrors, lenses and their combinations
Image:•real or virtual •erect or inverted•lager, smaller, or the same size as the object
ho = hi
5
7. Spherical mirror
1) Mirror equation
C di
do
h
fdd
fdd
io
oi
if
if
fdd i
111
0
focus
2
f
Rf
Example:
?
0.3
0.1
i
o
d
md
mR
mm
d
mmmdRd
i
i
6.00.5
0.3
0.3
0.5
0.3
1
0.1
2121
0
6
2) Magnification
Co
i
o
i
d
d
h
hm
dido
imageerect - 0 if
image inverted - 0 if
m
m
Example: What is magnification in the previous example?
2.00.3
6.0
m
m
d
dm
o
iThis image is real, inverted,and 5 times smaller than the object
7
3) Graphical method
8
4) Image and object at various distances
C F
C F
fdd i
111
0
focus
2
f
Rf
o
i
o
i
d
d
h
hm
0f=R/22f=R 9
magnification image mirror do di
m<0 inverted, real concave do>f di>f
m>1
0<m<1
upright, virtual concave
convex
0<do<f
0<do
di<0
-f<di<0
10
Example: You are standing 3.0 m from a convex security mirror in a store. You estimate the height of your image to be half of your actual height. Estimate the radius of curvature of the mirror.
o
i
o
i
d
d
h
hm
Rfdd i
2111
0
?
0.3
021
0
R
hh
md
i
021 dd i
Rdd o
221
0
mdR 0.62 0
11
Example: The magnification of a convex mirror is +0.65 for objects 2.2 m from the mirror. What is the focal length of this mirror?
4.1m.f
?
2.2
65.0
0
f
md
m
o
i
o
i
d
d
h
hm 0mdd i
fdd i
111
0
fmdd
111
00
fmd
m 11
0
165.0
2.265.0
10
m
m
mdf
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Example: A shaving/makeup mirror is designed to magnify your face by a factor of 1.33 when your face is placed 20.0 cm in front of it. (a)What type of mirror is it? (b) Describe the type of image that it makes of your face. (c) Calculate the required radius of curvature for the mirror.
i i
o o
h dm
h d
i 26.6cmd
80.6cmf
2 2 80.6cm 161cmR f
Solution:(a) To produce a larger image requires a concave mirror. (b) The image will be erect and virtual. (c)
fdd i
111
0
?
0.20
33.1
0
R
cmd
m
13
Example1: Concave spherical mirrors produce images which A) are always smaller than the actual object B) are always larger than the actual objectC) are always the same size as the actual objectD) could be smaller than, larger than, or the same size as the actual object, depending on the placement of the object
Example2: Convex spherical mirrors produce images which A) are always smaller than the actual object B) are always larger than the actual object C) are always the same size as the actual object D) could be larger than, smaller than, or the same size as the actual object, depending on the placement of the object
Example3: A single concave spherical mirror produces an image which is A) always virtual B) always realC) real only if the object distance is less than fD) real only if the object distance is greater than f
Example4: A single convex spherical mirror produces an image which is A) always virtual B) always real C) real only if the object distance is less than fD) real only if the object distance is greater than f
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