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Geometric Optics

Geometric Optics. Mirrors, light, and image formation. Geometric Optics. Understanding images and image formation, ray model of light, laws of reflection and refraction, and some simple geometry and trigonometry The study of how light rays form images with optical instruments.

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Geometric Optics

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  1. Geometric Optics Mirrors, light, and image formation

  2. Geometric Optics • Understanding images and image formation, ray model of light, laws of reflection and refraction, and some simple geometry and trigonometry • The study of how light rays form images with optical instruments

  3. Reflection and refraction on plane mirrors Reflection and Refraction at a plane Surface

  4. Key terms • Anything from which light rays radiate • Object • Anything from which light rays radiate that has no physical extent • Point object • Real objects with length, width, and height • Extended objects

  5. Key terms

  6. Key terms

  7. Image formation by a Plane mirror

  8. Image formation by a Plane mirror

  9. Reflection at a Plane Surface

  10. Image formation by a Plane mirror V θ θ θ θ M’ M s s’

  11. Image formation by a Plane mirror • M is the object and M’ is the virtual image • Ray MV is incident normally to the plane mirror and it returns along its original path • s= object distance • s’= image distance • s=-s’

  12. Image formation by a Plane mirror • Sign rules For the object distance: • When the object is on the same side of the reflecting or the refracting surface as the incoming light, s is positive For the image distance: • When the image is on the same side of the reflecting or the refracting surface as the outgoing light, s’ is positive

  13. Image of an extended object V’ V Q’ Q θ θ y y’ θ θ M θ M’ s s’

  14. Image of an extended object • Lateral magnification • Ratio of image height to object height • M=y’/y • Image is erect • m for a plane mirror is always +1 • Reversed means front-back dimension is reversed

  15. Reflection on Concave and Convex mirrors Reflection at a Spherical Surface

  16. Reflection at a Concave Mirror V C P P’

  17. Reflection at a Concave Mirror

  18. Graphical Methods for Mirrors Image formation on spherical mirrors

  19. Graphical Method • Consists of finding the point of intersection of a few particular rays that diverge from a point of the object and are reflected by the mirror • Neglecting aberrations, all rays from this object point that strike the mirror will intersect at the same point

  20. Graphical Method • For this construction, we always choose an object point that is not on the optic axis • Consists of four rays we can usually easily draw, called the principal rays

  21. Graphical Method

  22. Object is at F

  23. Object is between F and Vertex

  24. Object is at C

  25. Object is between C and F

  26. Positions of objects for concave mirrors

  27. Image formation by concave mirrors

  28. Reflection at a Concave Mirror

  29. Reflection at a Concave Mirror

  30. Reflection at a Concave Mirror V F C s at infinity s’= R/2

  31. Reflection at a Concave Mirror • All reflected rays converge on the image point • Converging mirror • If R is infinite, the mirror becomes plane

  32. Reflection at a Concave Mirror f= R/2

  33. Reflection at a Concave Mirror V F C s’ at infinity s= R/2

  34. Reflection at a Concave Mirror 1/s+ 1/s’= 1/f Object image relation, spherical mirror

  35. Image of an Extended Object

  36. Reflection at a Convex Mirror F C s’ or s= R/2 s or s’ at infinity

  37. Image formation on spherical mirrors • Sign rules For the object distance: • When the object is on the same side of the reflecting or the refracting surface as the incoming light, s is positive; otherwise, it is negative

  38. Image formation on spherical mirrors • Sign rules For the image distance: • When the image is on the same side of the reflecting or the refracting surface as the outgoing light, s’ is positive; otherwise, it is negative

  39. Image formation on spherical mirrors • Sign rules: For the radius of curvature of a spherical surface: • When the center of curvature C is on the same side as the outgoing light, the radius of curvature is positive, otherwise negative

  40. Reflection at a Convex Mirror • The convex side of the spherical mirror faces the incident light • C is at the opposite side of the outgoing rays, so R is neg. • All reflected rays diverge from the same point • Diverging mirror

  41. Reflection at a Convex Mirror

  42. Refraction at spherical interface Refraction at a Spherical Surface

  43. Refraction at a Spherical Surface C V

  44. Refraction at a Spherical Surface na/s + nb/s’=0 At a plane refracting surface

  45. Biconcave and biconvex thin lenses Graphical Method for Lenses

  46. Lenses

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