Geometric Optics Conceptual Quiz 23. Topics u The Ray Model of Light u Reflection u Formation of Images by Spherical Mirrors u Index of Refraction u Refraction.
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Geometric Optics
Conceptual Quiz 23
Topics
The Ray Model of Light Reflection Formation of Images by Spherical Mirrors Index of Refraction Refraction Total Internal Reflection Thin Lenses
The Ray Model of Light Reflection Formation of Images by Spherical Mirrors Index of Refraction Refraction Total Internal Reflection Thin Lenses
Conceptual Quiz 23
Light very often travels in straight lines. We represent light using rays, which are straight lines emanating from an object. This is an idealization, but is very useful for geometric optics.
The Ray Model of Light
Conceptual Quiz 23
Law of Reflection
The incident ray, the reflected ray, and the normal to the surface all lie in the same plane, and the angle of reflection r
equals the angle of
incidence i
i = r
mirror
Incidentray
reflectedray
normal
iθrθ
Reflection
Conceptual Quiz 23
Image in a Plane Mirror
Mirror
Object
Image
Reflection
Conceptual Quiz 23
Image in a Plane Mirror
Mirror
Object
do
di
Image
h
d
h
d oi
The image is as far behind the mirror as the object is in front of the mirror.
h
oi dd
Reflection
Conceptual Quiz 23
Image in a Plane MirrorMirror
Object
ho
doSimilar Triangles
hi
di
Image
Image is the same size as the object.
o
o
i
id
h
d
h oi hh
Reflection
Conceptual Quiz 23
Concave Mirror
Principle Focal Point
Formation of Images by Spherical Mirrors
2R
f
Conceptual Quiz 23
Concave Mirror
Light Source at the Focal Point
Formation of Images by Spherical Mirrors
Conceptual Quiz 23
Produces Parallel Rays of Light
Concave Mirror
Real Image
Formation of Images by Spherical Mirrors
Conceptual Quiz 23
Concave Mirror
do
di
f
ho
hi
f
fd
h
h i
o
i
Formation of Images by Spherical Mirrors
Conceptual Quiz 23
Concave Mirror
ho
hi
do
di
f
o
i
o
id
d
h
h
Formation of Images by Spherical Mirrors
Conceptual Quiz 23
f
fd
h
h i
o
i
o
i
o
id
d
h
h
io d1
d1
f1
io
iodd
ddf
Mirror Equation
o
iid
d
f
fd
Formation of Images by Spherical Mirrors
Conceptual Quiz 23
Concave Mirror
Virtual Image
Formation of Images by Spherical Mirrors
Conceptual Quiz 23
Concave Mirror
f
df
h
h i
o
i
do
f
ho
hi
di
Formation of Images by Spherical Mirrors
Conceptual Quiz 23
Concave Mirror
f
ho
hi
do di
o
i
o
id
d
h
h
Formation of Images by Spherical Mirrors
Conceptual Quiz 23
io d1
d1
f1
f
df
h
h i
o
i
o
i
o
id
d
h
h
o
iid
d
f
df
io d1
d1
f1
Formation of Images by Spherical Mirrors
Conceptual Quiz 23
Formation of Images by Spherical Mirrors
Problem 23-10
A mirror at an amusement park shows an upright image of any person who stands 1.4 m in front of it. If the image is three times the person’s height, what is the radius of curvature?
m 4.13Mdd oi
io d1
d1
f1
io
iodd
ddf or
m 2.4m 4.1
m 2.4m 4.1f
m 1.2
m 2.4 m 1.22f2r
o
i
o
id
d
h
hM
Conceptual Quiz 23
m 2.4di
Convex Mirror
Formation of Images by Spherical Mirrors
Conceptual Quiz 23
Concave Mirror
Formation of Images by Spherical Mirrors
f
do di
Conceptual Quiz 23
Concave Mirror
Formation of Images by Spherical Mirrors
do di
f
hohi
f
df
h
h i
o
i
Conceptual Quiz 23
Concave Mirror
Formation of Images by Spherical Mirrors
do di
hohi
o
i
o
id
d
h
h
Conceptual Quiz 23
f
df
h
h i
o
i
o
i
o
id
d
h
h
oi d1
f1
d1 io d
1d1
f1
Formation of Images by Spherical Mirrors
o
iid
d
f
df
Conceptual Quiz 23
Formation of Images by Spherical Mirrors
Problem 23-15
The image of a distant tree is virtual and very small when viewed in a curved mirror. The image appears to be 18 cm behind the mirror. What kind of mirror is it, and what is its radius of curvature?
io d1
d1
f1 cm 18f
cm 36 cm 812f2r
cm 1811
Conceptual Quiz 23
In general, light slows somewhat when traveling through a medium. The index of refraction of the medium is the ratio of the speed of light in vacuum to the speed of light in the medium:
Index of Refraction
vc
n
Conceptual Quiz 23
Problem 23-24
The speed of light in ice is 2.29 x 108 m/s.What is the index of refraction of ice?
Index of Refraction
vc
n m/s 10x 29.2
m/s 10x 00.38
8 31.1
Conceptual Quiz 23
Light changes direction when crossing a boundary from one medium to another. This is called refraction, and the angle the outgoing ray makes with the normal is called the angle of refraction.
Refraction
Conceptual Quiz 23
The angle of refraction depends on the indices of refraction, and is given by Snell’s law:
Refraction
1n
2n
1θ
2θ
2211 θsinnθsinn
air
water
Conceptual Quiz 23
Refraction
1n
2n
1θ
2θ
air
water
Conceptual Quiz 23
1v
2v
1λ
2λ
1f
2f
1
2n
n
2
1θsin
θsin
2
1v
v
2
1λ
λ 21 ff
2211 θsinnθsinn
Problem 23-32
Light is incident on an equilateral glass prism at a 45.0o angle to one face. Calculate the angle at which light emerges from the opposite face. Assume that n = 1.58.
Index of Refraction
α
β γo45
2θ3θ
4θ
n
air221air θsinnθsinn
2o θsin 58.145sin 00.1 o
2 6.26θ
o180γβα o
3oooo 180θ906.269060 o
3 6.33θ
4air3 θsinnθsinn
4o θsin 00.16.33sin 58.1 o
4 5.60θ
Apparent DepthRefraction
Conceptual Quiz 23
Apparent Depth
h
nw
na
w
ax
h’aw
a
w
w
an
n
θsin
θsin
wwaa θsinnθsinn Snell’s Law
From the diagram
hx
θtan
'hx
θtan
w
a
a
w
w
an
n
'hh
θtan
θtan
n
n h'h
w
a
Refraction
Conceptual Quiz 23
If light passes into a medium with a smaller index of refraction, the angle of refraction is larger. There is an angle of incidence for which the angle of refraction will be 90°; this is called the critical angle:
Total Internal Reflection
1n2n o90
cθ
o2c1 90sinnθsinn
Snell’s Law
1
o2
c n
90sinnθsin
1
2c n
nθsin
Conceptual Quiz 23
Thin lenses are those whose thickness is small compared to their radius of curvature. They may be either converging (a) or diverging (b).
Thin Lenses
Conceptual Quiz 23
Double Convex Lens
Focal Point
Thin Lenses
Conceptual Quiz 23
Real Image
Double Convex Lens
Thin Lenses
Conceptual Quiz 23
ho
Similar Triangles
Double Convex Lens
f f
do di
hi
f
fd
h
h i
o
i
Thin Lenses
Conceptual Quiz 23
Convex Lens
ho
hif f
do
Similar Triangles
di
o
i
o
id
d
h
h
Thin Lenses
Conceptual Quiz 23
Lens Equation
Double Convex Lens
f
fd
h
h i
o
i
o
i
o
id
d
h
h
io d1
d1
f1
Thin Lenses
o
iid
d
f
fd
Conceptual Quiz 23
Convex Lens
f f
di
ho
Similar Triangles
do
hi
f
fd
h
h i
o
i
Thin Lenses
Conceptual Quiz 23
Convex Lens
f f
hohi
Similar Triangles
di
do
o
i
o
id
d
h
h
Thin Lenses
Conceptual Quiz 23
Convex Lens
Lens Equation
f
fd
h
h i
o
i
o
i
o
id
d
h
h
io d1
d1
f1
Thin Lenses
o
iid
d
f
fd
Conceptual Quiz 23
Formation of Images by Spherical Mirrors
Magnification:
o
i
o
id
d
h
hM
Power:The unit for lens power is the diopter (D).
f1
P
A 30 cm focal length lens has a power
D 33.3m 30.0
1f1
P
Conceptual Quiz 23
Problem 23-44
Sunlight is observed to focus at a point 18.5 cm behind a lens.What kind of lens is it?
Index of Refraction
Pf1
d1
d1
io
What is its power in diopters?
Converging Lens
D 41.5 m 185.0
11P
Conceptual Quiz 23
Virtual Focal Point
Concave Lens
Thin Lenses
Conceptual Quiz 23
Concave Lens
Virtual Image
Thin Lenses
Conceptual Quiz 23
Concave Lens
ho
Similar Triangles
ho
hi
do
f
di
f
df
h
h i
o
i
Thin Lenses
Conceptual Quiz 23
Concave Lens
Similar Triangles
ho
hi
do
f
di
o
i
o
id
d
h
h
Thin Lenses
Conceptual Quiz 23
Concave Lens
Lens Equation
f
df
h
h i
o
i
o
i
o
id
d
h
h
io d1
d1
f1
Thin Lenses
o
iid
d
f
df
Conceptual Quiz 23
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