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Mathematical determination the mirror image

Mathematical determination the mirror image. MATHEMATICAL DETERMINATION OF DIAGRAM VALUES. VARIABLES. Mathematical Solution. h means height d means distance f means length between vertex and focal point i means image o means object. MAGNIFICATION. Magnification equations.

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Mathematical determination the mirror image

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  1. Mathematical determination the mirror image

  2. MATHEMATICAL DETERMINATION OF DIAGRAM VALUES

  3. VARIABLES

  4. Mathematical Solution h means height d means distance f means length between vertex and focal point i means image o means object

  5. MAGNIFICATION

  6. Magnification equations M = hi / ho M = -di / do

  7. Combine the equations M = hi / ho =-di / do hi / ho

  8. What does a negative value of magnification mean?

  9. Image is inverted (upside down on other side of PA)

  10. When are other values are negative Values are negative if : Distance is virtual, across the other side of the mirror from the object The focal length for a convex mirror, since it is on the other side of the mirror

  11. MIRROR EQUATION

  12. Mirror equation 1/f = 1/ di + 1/do

  13. Mirror equation Proof

  14. Both equations Proof through geometry Based on distances heights found in diagrams Approximate value, not exact

  15. Radius of curvature • Radius of curvature = distance from center point to vertex r = twice the focal length (f)

  16. When solving these problems • Make sure all units are the same, but do not worry if it is not in the standard metric units. • Watch for negative values in given units!!!

  17. Example problem A 3.00 cm tall object is 20.0 cm from a 16.0 cm radius concave mirror. A. Determine the image position B. Determine the image height

  18. About units • If all units are the same, do NOT convert. • Leave in cm, mm, m…

  19. Answer to part A • Radius of curvature = twice the focal length = 2f • 16 = 2f means f = 8 cm • The do = 20cm (given) • Use mirror equation: 1/8 = 1/20 + 1/di • Solve di = 13.3 cm, means image is real oand on same side as object

  20. Answer to part B • Ho = 3.0 • 3/Hi = -13.3 / 20 • Hi = -4.51 large and inverted than object

  21. Another example problem • An object 2.0 cm high is 30.0 cm from a concave mirror. The radius of curvature of the mirror is 20.0 cm. a. What is the location of the image? b. What is the size of image?

  22. 3rd example problem • If an object is 2.0 cm in height is 5.0 cm in front of a concave mirror of focal length 10.0 cm. Determine the size and location of the image. • Is image real/virtual and what is the orientation of image?

  23. Homework • In the text book • Pg 469 13-16 • Pg 472 17-21 • Odds should have answers in the back of the book

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