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The Mirror Equation.pptx

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The Mirror Equation.pptx

  1. 1. The Mirror Equation @ ATDC
  2. 2. Review 2 Identify the parts of a curved mirror. Principal Axis Center of Curvature (C) Focal Point/ Focus (F) Vertex (A) Radius of Curvature (R) Focal Length (f)
  3. 3. Review 3 Always remember that the focal length (f) is ½ of the radius of curvature (R) Radius of Curvature (R) Focal Length (f) f = ½R For example: if the radius of curvature is 40cm then the focal length (f) is 20cm. f = ½ (40cm) = 20cm
  4. 4. Summary for Concave Mirror 20XX Presentation title 4 When an object is: • Beyond C • At C • Between C and F • At F • Between F and mirror Image is: • Between C and F • At C • Beyond C • No image • Virtual image
  5. 5. Convex Mirror 20XX Presentation title 5
  6. 6. Ray Diagram for Convex Mirror 20XX Presentation title 6
  7. 7. Ray Diagram for Convex Mirror 20XX Presentation title 7 C F Always: Virtual, reduced, upright image
  8. 8. There is an important relationship between the distance of the object (do), the distance of the image (di), and the focal length (f). This relationship is known as the mirror equation. The mirror equation is an accurate way to find and describe the image formed by a spherical mirror through computation or via a mathematical method. 20XX Presentation title 8 The Mirror Equation
  9. 9. This relationship can be expressed using the equation; 20XX Presentation title 9 The Mirror Equation 𝟏 𝒇 = 𝟏 𝒅𝒐 + 𝟏 𝒅𝒊 where: f = focal length do = distance of the object Di = distance of the image
  10. 10. The mirror equation is applicable to both concave and convex mirrors. Given the following conditions: 20XX Presentation title 10 The Mirror Equation
  11. 11. m = 𝑺𝒊 𝑺𝒐 = 𝒅𝒊 𝒅𝒐 20XX Presentation title 11 The Mirror Equation The formula for magnification can be expressed using the formula: Where: Si = Size of the image sometimes express as hi (Height of the image) So = Size of the image sometimes express as ho (Height of the object)
  12. 12. Sample problem 1 A flower vase is placed 15cm in front of a concave mirror whose focal length is 10cm. Where is the image located? Describe the image. Given: do = 15cm f = 10cm Unknown: di = ? Formula: 𝟏 𝒇 = 𝟏 𝒅𝒐 + 𝟏 𝒅𝒊 Solution: (you may directly solve the problem by substituting the value of the given or you may derive first the formula) Answer: di = 33.33cm Substitute the value in the given formula then compute Transposition (Note the sign) Compute for the value Cross multiply Divide both sides to proceed with the cancellation Compute
  13. 13. 20XX Presentation title 13 di = 33.33cm m = 𝑺𝒊 𝑺𝒐 = 𝒅𝒊 𝒅𝒐 For magnification Image real, inverted, and enlarge
  14. 14. 20XX Presentation title 14 Sample problem 2 A bottle is held 5.0cm from a concave mirror whose radius is 28.0cm. At what distance will the image be formed? Sample problem 3 A cup is placed in front of a curved mirror whose focal point is at 8cm, and formed an image 24cm beyond C. At what point thus the cup is located?

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