Question

How far should an object be from a concave mirror of radius 30cm to form a real image 1/6 of its size?

Answer 1

Answer on Question #47670-Engineering-Other

How far should an object be from a concave mirror of radius 30cm to form a real image 1/6 of its size?

Solution

$$f = \frac {R}{2} = \frac {30 \mathrm{cm}}{2} = 15 \mathrm{cm}.$$

The image is real and reduced, so it is inverted too. The magnification is

$$M = - \frac {d _ {i}}{d _ {o}} = - \frac {1}{6} \rightarrow d _ {i} = \frac {1}{6} d _ {o}.$$ $$\frac {1}{f} = \frac {1}{d _ {o}} + \frac {1}{d _ {i}} \rightarrow \frac {1}{f} = \frac {1}{d _ {o}} + \frac {6}{d _ {o}} = \frac {7}{d _ {o}} \rightarrow d _ {o} = 7 f = 7 \cdot 15 \mathrm{cm} = 105 \mathrm{cm}.$$

Answer: 105 cm.

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