Lens Image Distance Example

GeoGebra Commands & Parameters

1. LaTeX(steps) → counter
2. LaTeX("\text{Move the slider to solve the problem.}") → text0
3. Corner(1) → A
4. Corner(3) → B
5. Point(xAxis) → D
6. CircumcircleArc(C, D, F_1) → c
7. CircumcircleArc(I, J, H) → d
8. CircumcircleArc(G, D, E) → e
9. CircumcircleArc(E, J, G) → f
10. Segment(C, H) → b
11. Segment(F_1, I) → g
12. If(sgn(focal) < 0, "f<0", "f>0") → focaltext
13. Vector((0, -1.25), (x(F), (-1.25))) → u
14. Midpoint((0, -1.25), (sgn(focal), (-1.25))) → M
15. LaTeX("d_{image}<0") → imagetextneg
16. Vector((0, -1.77), (-1.5, -1.77)) → v
17. Midpoint((0, -1.77), (-1.5, -1.77)) → N
18. Vector((0, -1.73), (1.5, -1.73)) → w
19. Midpoint((0, -1.73), (1.5, -1.73)) → O
20. LaTeX("d_{image}>0") → imagetextpos
21. Vector((0, 1.23), (-1.5, 1.23)) → h
22. Midpoint((0, 1.23), (-1.5, 1.23)) → P
23. Vector((0, 1.27), (1.5, 1.27)) → i
24. Midpoint((0, 1.27), (1.5, 1.27)) → Q
25. LaTeX("d_{object}>0") → objecttextpos
26. LaTeX("d_{object}<0") → objtextneg
27. Line((-1, 0), (1, 0)) → j
28. Line((0, -1), (0, 1)) → k
29. LaTeX("\textcolor{#000099}{f=\frac{d_{object}d_{image}}{d_{object}+d_{image}}}") → text3
30. If(focal < 0, LaTeX[("-d_{object}+" * diff)], LaTeX[("d_{object}+" * diff)]) → drelation
31. LaTeX((((("\textcolor{#000099}{f=" * focal) * "}\cr\textcolor{#000099}{d_{image}= ") * drelation) * "}")) → Problem
32. If(focal < 0, LaTeX[diff], LaTeX[("2d_{object}+" * diff)]) → denominator
33. If(focal < 0, LaTeX[(("-d_{object}^2+" * diff) * "d_{object}")], LaTeX[(("d_{object}^2+" * diff) * "d_{object}")]) → numerator
34. LaTeX((("\text{Multiply both sides by }\textcolor{#000099}{" * denominator) * "}.")) → text8
35. If(focal < 0, LaTeX[(focal * diff)], LaTeX[(((focal * 2) * "d_{object}+") * focaldiff)]) → leftside
36. LaTeX((((((("\textcolor{#000099}{" * focal) * "=\frac{") * numerator) * "}{") * denominator) * "}}")) → text7
37. LaTeX((((("\textcolor{#000099}{" * leftside) * "=") * numerator) * "}")) → text9
38. If(focal < 0, LaTeX[(("\text{Subtract }\textcolor{#000099}{" * numerator) * "}\text{ from both sides.}")], LaTeX[(("\text{Subtract }\textcolor{#000099}{" * leftside) * "}\text{ from both sides.}")]) → text10
39. If(focal < 0, LaTeX[(((("\textcolor{#000099}{d_{object}^2-" * diff) * "d_{object}") * leftside) * "=0}")], LaTeX[(((("\textcolor{#000099}{d_{object}^2 +(" * linterm) * ")d_{object}-") * focaldiff) * "=0}")]) → text11
40. LaTeX("\text{}") → text14
41. If(focal < 0, Polynomial[x^(2) - (diff * x) + (focal * diff)], Polynomial[x^(2) + ((diff - (2 * focal)) * x) - (focal * diff)]) → p
42. Unique(Zip[x(a), a, zeropts]) → zeros
43. Length(zeros) → numzeros
44. If(Element[zeros, Length[zeros]] ≟ 0 ∨ Element[zeros, 1] ≟ 0, LaTeX["\text{A zero value for }\textcolor{#000099}{d_{object}}\text{ makes no}\cr\text{sense because the object will be in the}\cr\text{middle of the lens.}"], "") → zeroroot
45. If(Element[zeros, 1] < 0, LaTeX["\text{A negative value for }\textcolor{#000099}{d_{object}}\text{ means the object is on}\cr\text{the right side of the lens. This is a virtual object}\cr\text{which typically occurs only in multi-lens systems.}\cr"], "") → negroot
46. If(Element[zeros, Length[zeros]] > 0, LaTeX["\text{A positive value for }\textcolor{#000099}{d_{object}}\text{ means the object is on}\cr\text{the left side of the lens.}\cr"], "") → posroot
47. LaTeX(((negroot * posroot) * zeroroot)) → text17
48. LaTeX("\textcolor{#000099}{x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}}") → text20
49. If(focal < 0, (focal * diff), ((-focal) * diff)) → quadc
50. If(focal < 0, (-diff), diff - (2 * focal)) → quadb
51. LaTeX((((((("\textcolor{#000099}{d_{object}=\frac{-(" * quadb) * ")\pm\sqrt{(") * quadb) * ")^2-4(1)(") * quadc) * ")}}{2(1)}}")) → text22
52. LaTeX("\text{Simplify.}") → text23
53. LaTeX((("\textcolor{#000099}{d_{object}=" * zeros) * "}")) → text24
54. If(focal > 0, Zip[a + diff, a, zeros], Zip[(-a) + diff, a, zeros]) → images
55. LaTeX("\text{Find }\textcolor{#000099}{d_{image}}\text{ and interpret the result in terms of the}\cr\text{image location relative to the lens.}") → text25
56. LaTeX((("\textcolor{#000099}{d_{image}=" * images) * "}")) → text26
57. If(Min[images] < 0, LaTeX["\text{A negative value for }\textcolor{#000099}{d_{image}}\text{ means the image is on}\cr\text{the left side of the lens.}\cr"], "") → negimage
58. If(Max[images] > 0, LaTeX["\text{A positive value for }\textcolor{#000099}{d_{image}}\text{ means the image is on}\cr\text{the right side of the lens.}\cr"], "") → posimage
59. If(Element[images, Length[images]] ≟ 0 ∨ Element[images, 1] ≟ 0, LaTeX["\text{A zero value for }\textcolor{#000099}{d_{image}}\text{ makes no sense because}\cr\text{the image will be in the middle of the lens.}"], "") → zeroimage
60. LaTeX(((negimage * posimage) * zeroimage)) → text27
61. Vector(((-Element[zeros, chooseSolution]), 0), ((-Element[zeros, chooseSolution]), 1)) → l
62. Vector((Element[images, chooseSolution], 0), (Element[images, chooseSolution], ((-Element[images, chooseSolution])) / Element[zeros, chooseSolution])) → m
63. LaTeX((((("\textcolor{#000099}{d_{object}=" * Element[zeros, chooseSolution]) * "}\cr \textcolor{#006633}{d_{image}=") * Element[images, chooseSolution]) * "}")) → text28
64. Vector((((-1.5) * abs(focal)), 0.5), (((-0.5) * abs(focal)), 0.5)) → n
65. Vector((((-1.5) * abs(focal)), (-0.5)), (((-0.5) * abs(focal)), (-0.5))) → q
66. LaTeX("\text{Use the buttons below to return to the original problem or}\cr\text{randomly generate a similar practice problem.}") → RandomizationText
67. LaTeX("\text{Substitute the defined variables into the thin lens equation and simplify.}") → text1
68. LaTeX("\text{Given function}") → text2
69. LaTeX((((((("\textcolor{#000099}{(" * focal) * ")=\frac{d_{object}(") * drelation) * ")}{d_{object}+(") * drelation) * ")}}")) → text5
70. If(focal < 0, LaTeX[(((("\text{Graph the simplified equation }\cr\textcolor{#000099}{d_{object}^2-" * diff) * "d_{object}") * leftside) * "=0}.")], LaTeX[(((("\text{Graph the simplified equation }\textcolor{#000099}{d_{object}^2 +(" * linterm) * ")d_{object}-") * focaldiff) * "=0}.")]) → text13
71. LaTeX("\text{Describe the zeros of the function and what that implies for the number of }\cr\text{possible solutions for }\textcolor{#000099}{d_{object}}\text{ and }\textcolor{#000099}{d_{image}.}") → text15
72. LaTeX((((((("\text{There are " * numzeros) * " possible positions for the object so that}\cr\textcolor{#000099}{d_{image}=") * drelation) * "}\text{ is true for a focal length of }\textcolor{#000099}{f=") * focal) * "}.")) → text16
73. LaTeX("\text{Quadratic formula}") → text19
74. LaTeX((((("\text{Substitute }\textcolor{#000099}{d_{object}}\text{ for }\textcolor{#000099}{x}\text{, }\cr\textcolor{#000099}{1}\text{ for }\textcolor{#000099}{a}\text{, }\textcolor{#000099}{" * quadb) * "}\text{ for }\textcolor{#000099}{b}\text{,}\cr\text{and }\textcolor{#000099}{") * quadc) * "}\text{ for }\textcolor{#000099}{c}.")) → text21
75. LaTeX("\text{Solve the simplified formula for }\textcolor{#000099}{d_{object}.}") → text18
76. LaTeX((((("\text{Substitute the given focal length, }\textcolor{#000099}{f=" * focal) * "}\text{,}\cr\text{and the relationship between the image and}\cr\text{object distances, }\textcolor{#000099}{d_{image}=") * drelation) * "}.")) → text4
77. LaTeX("\text{Simplify the numerator and denominator.}") → text6
78. If(focal < 0, LaTeX[(((("\text{The simplified function can be written as }\cr\textcolor{#000099}{d_{object}^2-" * diff) * "d_{object}") * leftside) * "=0}\text{.}")], LaTeX[(((("\text{The simplified function can be written as }\cr\textcolor{#000099}{d_{object}^2 +(" * linterm) * ")d_{object}-") * focaldiff) * "=0}\text{.}")]) → text12
79. LaTeX("\text{Move the slider to change the object's location.}") → text29