Chapter 23 Quiz
ÎWhich
‹ (1)
‹ (2)
‹ (3)
‹ (4)
‹ (5)
of the following is not a principal ray?
1
2
3
4
All are principal rays
PHY2054: Chapter 23
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Concave and Convex Mirrors
R
f =
2
PHY2054: Chapter 23
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Images from Mirrors
Location
C
f
Size
1 1 1
+ =
p q f
h′
q
M ≡ =−
h
p
q > 0 along reflected ray
PHY2054: Chapter 23
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Mirror Example
¾ 2 cm tall object (h = 2), 80 cm from mirror (p = 80)
¾ Mirror: 100 cm radius of curvature concave towards object (R = +100)
1 1 1
+ =
⇒ q = 133.3
80 q 50
M =−
133.3
q
=−
= −1.67
80
p
3
1
h′ = ( −1.67 ) h = −3.33
C
f
2
Roughly agrees with ray diagram (good to check it)
PHY2054: Chapter 23
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Images Formed by Refraction
n1 n2 n2 − n1
+
=
p q
R
n1q
h′
M = =−
h
n2 p
PHY2054: Chapter 23
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Image from Flat Refractive Surface
R=∞
n1 n2
n2
+
=0⇒q =− p
p q
n1
n1q
M =−
= +1
n2 p
Same size virtual image!
PHY2054: Chapter 23
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Example: Image in Pool
n1 = 1.333
n2 = 1.0
n2
q=− p
n1
1
q=−
p ≅ −0.75 p
1.333
So depth of image is about
3/4 depth of object
PHY2054: Chapter 23
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Atmospheric Refraction
¾
¾
Refraction in atmosphere makes sun always appear higher in sky
Can see the sun even when it is below the horizon!
PHY2054: Chapter 23
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Atmospheric Refraction Causes Various Mirages
PHY2054: Chapter 23
9
Approaching Car on Hot Road
PHY2054: Chapter 23
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Floating Iceberg! Cold Air, Warm Water
PHY2054: Chapter 23
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“Squashed” Sun Setting Over Ocean
PHY2054: Chapter 23
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Thin Lenses
PHY2054: Chapter 23
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Thin Lenses
f
f
Converging Lens
Rays parallel to axis refract
and pass through focal point
f>0
f
f
Diverging Lens
Rays parallel to axis refract and
appear to emerge from focal point
f<0
PHY2054: Chapter 23
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Location and Size of Image (Recall Mirror)
h′
q
M ≡ =−
h
p
1 1 1
+ =
p q f
PHY2054: Chapter 23
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Finding Image from Lens: Example
¾ f = 10 cm
¾ p = 30 cm
¾ h = 4 cm
1 1 1
+ = ⇒ q = +15cm
30 q 10
q
15
M = − = − = −0.5
30
p
h′ = −2cm
PHY2054: Chapter 23
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Principal Ray Diagrams for Lenses
q>0
PHY2054: Chapter 23
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Principal Ray Diagrams for Lenses (cont)
q<0
PHY2054: Chapter 23
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Principal Ray Diagrams for Lenses (cont)
q<0
PHY2054: Chapter 23
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Calculating Focal Length for Thin Lenses
⎛ 1
1
1 ⎞
= ( n − 1) ⎜ −
⎟
f
R
R
⎝ 1
2⎠
Lensmaker’s equation
Sign convention
R>0
R<0
PHY2054: Chapter 23
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Calculating Focal Length Example
Let n = 1.5, R = 10
1
1 ⎞
⎛1
= 0.5 ⎜ −
⎟ = 0.05
f
⎝ 10 ∞ ⎠
1
1 ⎞
⎛1
= 0.5 ⎜ −
⎟ = 0.1
f
⎝ 10 −10 ⎠
1
1 ⎞
⎛1
= 0.5 ⎜ −
⎟ = 0.1
f
⎝ 10 −10 ⎠
So f1 = f2/2
1 has twice the “power” of 2
PHY2054: Chapter 23
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Quiz on Lenses
Î All
the lenses below have either flat
sides or radius of curvature R.
Rank in descending order the value
of 1/f (lens power), i.e. from most
positive to most negative
⎛ 1
1
1 ⎞
= ( n − 1) ⎜ −
⎟
f
R
R
2⎠
⎝ 1
(1)
‹ (2)
‹ (3)
‹ (4)
‹ (5)
‹
A, C, B, E, D
C, A, D, B, E
B, A, C, E, D
D, E, B, C, A
C, A, E, D, B
Each term adds to lens power
Flat
A
B
C
D
PHY2054: Chapter 23
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22
Quiz on Mirrors
ÎAn
upright object is located in front of a convex mirror a
distance greater than the focal length. The image formed
by the mirror is:
‹ (1)
‹ (2)
‹ (3)
‹ (4)
‹ (5)
real, inverted, and smaller than the object
virtual, inverted, and larger than the object
real, inverted, and larger than the object
real, erect, and larger than the object
virtual, erect, and smaller than the object
1 1 1
= −
q f p
f < 0, so q < 0
M = −q/p < +1
PHY2054: Chapter 23
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