1. Geometric Optics
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2. Topics The Ray Model of Light The Ray Model of Light Reflection
Formation of Images by Spherical Mirrors
Index of Refraction
Refraction
Total Internal Reflection
Thin Lenses
Reflection
Formation of Images by Spherical Mirrors
Index of Refraction
Refraction
Total Internal Reflection
Thin Lenses
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3. The Ray Model of Light
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.
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4. Reflection Law of Reflection
reflected
ray
Law of Reflection
normal
Incident
ray
The incident ray, the reflected ray, and the normal to the surface all lie in the same plane, and the angle of reflection qr equals the angle of incidence qi
mirror
qi = qr
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5. Reflection Image in a Plane Mirror Mirror Object Image
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6. Reflection Image in a Plane Mirror Mirror q f h q f di Image Object do
The image is as far behind the mirror as the object is in front of the mirror.
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7. Image is the same size as the object.
Reflection
Image in a Plane Mirror
Mirror do f hi di
Image
Similar Triangles q f
Object ho
Image is the same size as the object.
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8. Formation of Images by Spherical Mirrors
Concave Mirror
Principle Focal Point
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9. Formation of Images by Spherical Mirrors
Concave Mirror
Light Source at
the Focal Point
Produces Parallel Rays of Light
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10. Formation of Images by Spherical Mirrors
Concave Mirror
Real Image
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11. Formation of Images by Spherical Mirrors
Concave Mirror do di f ho hi
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12. Formation of Images by Spherical Mirrors
Concave Mirror do di f ho hi
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13. Formation of Images by Spherical Mirrors
Mirror Equation
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14. Formation of Images by Spherical Mirrors
Concave Mirror
Virtual Image
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15. Formation of Images by Spherical Mirrors
Concave Mirror do f ho hi di
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16. Formation of Images by Spherical Mirrorsho hi do di
Concave Mirror
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17. Formation of Images by Spherical Mirrors
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18. 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?
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19. Formation of Images by Spherical Mirrors
Convex Mirror
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20. Formation of Images by Spherical Mirrors
Concave Mirror di do f
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21. Formation of Images by Spherical Mirrors
Concave Mirror ho hi do di f
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22. Formation of Images by Spherical Mirrors
Concave Mirror ho hi do di
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23. Formation of Images by Spherical Mirrors
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24. 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?
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25. Index of Refraction
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:
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26. The speed of light in ice is 2.29 x 108 m/s.
Index of Refraction
Problem 23-24
The speed of light in ice is 2.29 x 108 m/s.
What is the index of refraction of ice?
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27. Refraction
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.
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28. Refraction
The angle of refraction depends on the indices of refraction, and is given by Snell’s law:
air
water
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29. Refraction
air
water
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30. Index of Refraction
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. n
air

31. Refraction
Apparent Depth
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32. Refraction Apparent Depth x qa na Snell’s Law nw h’ qa qw h qw
From the diagram
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33. Total Internal Reflection
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:
Snell’s Law
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34. Thin Lenses
Thin lenses are those whose thickness is small compared to their radius of curvature. They may be either converging (a) or diverging (b).
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35. Thin Lenses
Double Convex Lens
Focal Point
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36. Thin Lenses
Double Convex Lens
Real Image
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37. Thin Lenses Double Convex Lens do di Similar Triangles ho f hi
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38. Thin Lenses Convex Lens do di Similar Triangles ho f f hi
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39. Thin Lenses Lens Equation
Double Convex Lens
Lens Equation
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40. Thin Lenses Convex Lens f f Similar Triangles ho hi do di
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41. Thin Lenses Convex Lens f f Similar Triangles ho hi di do
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42. Thin Lenses Lens Equation
Convex Lens
Lens Equation
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43. Formation of Images by Spherical Mirrors
Magnification:
Power:
The unit for lens power is the diopter (D).
A 30 cm focal length lens has a power
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44. Sunlight is observed to focus at a point 18.5 cm behind a lens.
Index of Refraction
Problem 23-44
Sunlight is observed to focus at a point 18.5 cm behind a lens.
What kind of lens is it?
Converging Lens
What is its power in diopters?
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45. Thin Lenses
Concave Lens
Virtual Focal Point
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46. Thin Lenses
Concave Lens
Virtual Image
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47. Thin Lenses Concave Lens f Similar Triangles ho ho hi di do
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48. Thin Lenses Concave Lens f Similar Triangles ho hi di do
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49. Thin Lenses Lens Equation
Concave Lens
Lens Equation
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