Question

An object placed in front of a convex mirror of radius 20cm produces an erect image which is one-fifth the size of the object. How far is the object from the mirror?

Answer 1

Answer on Question #47671-Engineering-Other

An object placed in front of a convex mirror of radius 20cm produces an erect image which is one-fifth the size of the object. How far is the object from the mirror?

Solution

$$f = - \frac {R}{2} = - \frac {20 \mathrm{cm}}{2} = - 10 \mathrm{cm}.$$

The magnification is $M = -\frac{d_i}{d_o} = \frac{1}{5} \rightarrow d_i = -\frac{1}{5} d_o$.

$$\frac {1}{f} = \frac {1}{d _ {o}} + \frac {1}{d _ {i}} \rightarrow \frac {1}{f} = \frac {1}{d _ {o}} - \frac {5}{d _ {o}} \rightarrow - \frac {1}{10 \mathrm{cm}} = - \frac {4}{d _ {o}} \rightarrow d _ {o} = 40 \mathrm{cm}.$$

Answer: 40 cm.

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