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02 – Concave or Converging Mirrors

Unit 3 – Light & Optics . 02 – Concave or Converging Mirrors. Remember the Diagram & Components of Concave Mirrors. v. Image Characteristics for Concave Mirrors. There are five (5) different situations, depending on where the object is located. Image Characteristics for Concave Mirrors.

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02 – Concave or Converging Mirrors

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  1. Unit 3 – Light & Optics 02 – Concave or Converging Mirrors

  2. Remember the Diagram & Components of Concave Mirrors v

  3. Image Characteristics for Concave Mirrors • There are five (5) different situations, depending on where the object is located

  4. Image Characteristics for Concave Mirrors • 1) Object is located BEYOND “C” • Image will be located between C and F • Image is inverted • Upside down • Magnification is less than 1.0 • Image is smaller than the object • Image is real • Light rays converge at the image location • You could place a sheet of paper at the image location and view the image on the paper

  5. Image Characteristics for Concave Mirrors • 2) Object is located at “C” • Image will also be located at “C” • Image is inverted • Upside down • Magnification is 1.0 • Image is same size as object • Image is real • Light rays converge at the image location • You could place a sheet of paper at the image location and view the image on the paper

  6. Image Characteristics for Concave Mirrors • 3) Object is located between “C” and “F” • Image located beyond C • Image is inverted • Upside down • Magnification is greater than 1.0 • Image is larger than the object • Image is real • Light rays converge at the image location • You could place a sheet of paper at the image location and view the image on the paper

  7. Image Characteristics for Concave Mirrors • 4) Object is located at “F” • No image is formed • After reflecting the light rays are travelling parallel to each other and will not produce an image

  8. Image Characteristics for Concave Mirrors • 5) Object is located in front of “F” • Image is located somewhere on the opposite side of the mirror (inside the mirror) • Image is erect • Right side up • Magnification is greater than 1.0 • Image is larger than the object • Image is virtual • Light rays do not actually converge on the location • Any attempt to project the image on a sheet of paper would not be possible since light does not pass through the location

  9. Locating Images using Math • A ray diagram helps determine the approximate location and size of the image.   • To obtain numerical information, we can use the Mirror equation and the Magnification equation.

  10. The Mirror Equation • The mirror equation expresses the quantitative relationship between the object distance (do), the image distance (di), and the focal length (f). • Where: • do: is the distance from the object to the mirror (vertex) • di: is the distance from the image to the mirror • f: is the focal length (½c)

  11. The Magnification Equation • The Magnification equation relates the ratio of the image distance and object distance to the ratio of the image height (hi) and object height (ho). • Since M = hi/ho or (-)di/do, the negative sign is necessary so that we get a negative (-) value indicating the image is inverted • Remember, we often have inverted images with converging mirrors.

  12. SIGN CONVENTIONS: • f is + if the mirror is a concave mirror (converging) • f is - if the mirror is a convex mirror (diverging) • di is + if the image is a real image and located on the object's side of the mirror. • di is - if the image is a virtual image and located behind the mirror. • hi is + if the image is an upright image (and therefore, also virtual) • hi is - if the image an inverted image (and therefore, also real)

  13. Examples • 1) An object 5.0 cm tall is placed 22.0 cm in front of a converging mirror with a radius of curvature of 30.6 cm. Determine the image distance and the image size. • Known info: • do = 22.0cm • Radius = 30.6 so f = ½ R  15.3cm

  14. Examples • 2) The same object as before is placed in front of the same mirror, this time at a distance of 8.2 cm from the mirror. Determine the image distance and the image size.

  15. Extra Examples • 3)An object is located 30.0 cm from a converging mirror with a focal length of 5.0 cm.a) Where will the image be formed?Known information: • f = 5.0 cm • do = 30.0 cm • ho = 4.0 cm

  16. Extra Examples • b) What is the magnification? • The image is smaller and inverted - negative sign.

  17. Extra Examples • c) If the object is 4.0 cm tall, how tall is the image? • The image is inverted because hi is negative.

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