Question

A reflecting, spherical Christmas tree ornament has a diameter of 7.0 cm. A child looks at the ornament from a distance of 28 cm. Describe the image she sees.
Answer: -1.65cm
How? I've tried many methods, even the one on here but am still getting a way different number.

Answer 1

Answer on Question #58967-Physics-Optics

A reflecting, spherical Christmas tree ornament has a diameter of 7.0 cm. A child looks at the ornament from a distance of 28 cm. Describe the image she sees.

Solution

A focal length of the mirror is

$$f = \frac {R}{2} = \frac {D}{4} = \frac {7.0 \text{ cm}}{4} = 1.75 \text{ cm}.$$

We need substitute $-f$ in the mirror equation because the mirror is convex.

$$\frac {1}{o} + \frac {1}{i} = - \frac {1}{f} \rightarrow \frac {1}{28} + \frac {1}{i} = - \frac {1}{1.75}$$ $$i = \frac {1}{- \frac {1}{1.75} - \frac {1}{28}} = -1.65 \text{ cm}.$$

Answer: -1.65 cm.

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