Calculating Magnification of Christmas Tree Ornament

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SUMMARY

The discussion focuses on calculating the magnification of a spherical Christmas tree ornament with a diameter of 4.76 cm when an object is placed 11.9 cm away. The focal length (f) is determined to be 1.19 cm using the formula f = 0.5 * r, where r is the radius. The image distance (di) is calculated using the lens formula (1/di) + (1/do) = 1/f, resulting in di = 1.32222 cm. The magnification (m) is then computed as m = -(di/do), yielding a value of -0.1111.

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  • Understanding of spherical mirrors and their properties
  • Familiarity with the lens formula (1/di + 1/do = 1/f)
  • Knowledge of magnification calculations (m = -di/do)
  • Basic geometry related to circles and spheres
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  • Study the characteristics of concave and convex mirrors
  • Explore the implications of negative magnification in optics
  • Learn about the applications of spherical mirrors in real-world scenarios
  • Investigate the effects of object distance on image formation
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Kris1120
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Homework Statement



A spherical Christmas tree ornament is
4.76 cm in diameter.
What is the magnification of the image of
an object placed 11.9 cm away from the ornament?

Homework Equations



f = .5* r

(1/di) + (1/do) = 1/f

m=-(di/do)

The Attempt at a Solution



f = .5*2.38 = 1.19 cm

(1/di) = (1/1.19) - (1/11.9) = 1.32222 cm

m =-(1.32222/11.9) = -0.1111
 
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Hi Kris1120,

Kris1120 said:

Homework Statement



A spherical Christmas tree ornament is
4.76 cm in diameter.
What is the magnification of the image of
an object placed 11.9 cm away from the ornament?

Homework Equations



f = .5* r

(1/di) + (1/do) = 1/f

m=-(di/do)

The Attempt at a Solution



f = .5*2.38 = 1.19 cm

I don't believe this is right. What type of mirror is this? What does that tell you about the focal length?
 

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