Introductory Physics Volume Two

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170 Geometric Optics 8.7 -x i x o f f Notice that we still use the three principle rays. The topmost ray in the figure above strikes the lens as if it came from the focal point. The dotted line going back to the focal point is an extension of the actual path of the light ray. Notice also that even though the ray constructed in this manner does not hit the lens (since the lens was not tall enough) we can still use the ray to construct the location of the image. The thin lens and magnification equations can still be used in this case, but in order to get the algebra to work out correctly you need to interpret a negative image distance (x i ) as being on the side of the lens where the light originates from. Example Suppose that in the figure above x 0 = 6cm, y 0 = 2.0cm and f = 9cm. Putting this into the thin lens equation we find 1 6cm + 1 = 1 x i 9cm −→ 1 = 1 x i 9cm − 1 6cm = − 1 18cm −→ x i = −18cm Now we can use the magnification equation to find the size of the image. y i = − y o −→ y i = − x i y o = − −18 (2cm) = 6.0cm x i x o x o 6 ⊲ Problem 8.4 You have a lens with a focal length of 80cm. You place an object at 60cm from the lens. The object is 3cm tall. (a) Construct the image location using the principle rays. (b) Find the location of the image using the thin lens equation. (c) Find the height of the image from the magnification equation. ⊲ Problem 8.5 For a converging lens with a focal length of f, over what range of object distances is the image: (a) real?
8.8 Diverging Lenses 171 (b) virtual? (c) upright? (d) inverted? (e) larger than the object? § 8.8 Diverging Lenses Now consider what happens when parallel rays strike a lens that is thiner in the middle. The rays diverge from the optical axis as if they came from the focal point on the incident side. This type of lens is called a Diverging Lens. This is drawn in the figure below. -f We might also consider what happens to rays that are converging toward the focal point on the far side of the lens, these rays exit the lens parallel to the optical axis, as indicated in the diagram below. -f We can, as before, construct the location and size of the image, by using three principle rays. The three rays are, (1) a ray that leaves the object parallel to the optical axis, (2) a ray going through the center of the lens, (3) a ray that leaves the object headed toward the focal point on the far side of the lens. This has been done in the figure below.
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1 Introductory Physics Volume Two S
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1.1 Electric Charge 3 Demo 1 Electr
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1.1 Electric Charge 5 Then charge a
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- - - - - 1.2 Coulomb’s Law 7 How
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1.2 Coulomb’s Law 9 Example Consi
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1.3 Electric Field 11 + - Compute t
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1.3 Electric Field 13 points a well
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1.3 Electric Field 15 Look back now
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1.5 Continuous Charge Distributions
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1.6 Gauss’s Law 19 § 1.6 Gauss
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1.6 Gauss’s Law 21 Suppose that y
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1.7 More Examples 23 ⊲ Problem 1.
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1.7 More Examples 25 The net force
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1.7 More Examples 27 out the net fo
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1.7 More Examples 29 -4q +2q -q E -
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1.7 More Examples 31 The area vecto
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1.8 Homework 33 ⊲ Problem 1.14 Ri
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1.9 Summary 35 § 1.9 Summary Defin
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2.1 Electric Potential 37 2 Electri
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2.1 Electric Potential 39 Example S
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2.2 Equipotentials 41 ⊲ Problem 2
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2.3 Conductors in Equilibrium 43
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2.4 Capacitors 45 § 2.4 Capacitors
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2.5 Energy in an Electric Field 47
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2.7 More Examples 49 ⊲ Problem 2.
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2.7 More Examples 51 The resulting
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2.8 Homework 53 add up potential du
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2.8 Homework 55 ⊲ Problem 2.27 Ho
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3.2 Electric Current 57 3 Circuits
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3.3 Ohm’s Law 59 Some materials,
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3.5 Kirchhoff’s Rules 61 ⊲ Prob
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3.6 Resistors in Combination 63 par
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3.8 Capacitor Circuits 65 Theorem:
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3.9 More Examples 67 Note that the
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3.9 More Examples 69 This mean that
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3.9 More Examples 71 15Ω 5Ω 10Ω
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3.9 More Examples 73 First combine
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3.10 Homework 75 ⊲ Problem 3.16 B
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3.10 Homework 77 4 µF + - 2 µF +
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3.11 Summary 79 § 3.11 Summary Def
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4.2 Magnetic Force on a Current 81
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4.3 Trajectories Under Magnetic For
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4.4 Lorentz Force 85 with a charge
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4.5 Hall Effect 87 But this charge
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4.6 More Examples 89 -e F E v F B =
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4.6 More Examples 91 The force on t
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4.7 Homework 93 Imagine the closed
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4.7 Homework 95 circular orbits. Wr
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5.1 Sources of Magnetic Field 97 5
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5.1 Sources of Magnetic Field 99
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5.2 Ampere’s Law 101 and ⃗ dr s
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5.2 Ampere’s Law 103 This satisfi
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5.4 More Examples 105 distance r fr
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5.4 More Examples 107 up the integr
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5.4 More Examples 109 Use the Biot-
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5.5 Homework 111 The magnetic force
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5.5 Homework 113 3.00 A 1.00 A 1 mm
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6.2 Faraday’s Law 115 6 Time Vary
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6.2 Faraday’s Law 117 Definition:
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Page 187 and 188: B Index 187 † Ohm’s Law: Resist
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Page 191 and 192: C Power Series Expansions 191 The F
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Introductory Physics Volume Two

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