Question

An object 10 cm in front of a concave mirror forms an image
5 cm behind the mirror. What is the focal length of the mirror?

Answer 1

Answer on Question#65152, Physics / Optics

Question

An object $10\,\mathrm{cm}$ in front of a concave mirror forms an image $5\,\mathrm{cm}$ behind the mirror. What is the focal length of the mirror?

Solution

Location of image behind a concave mirror implies that we have the case when object is between focal point and mirror (image magnified).

$$\frac{1}{f} = \frac{1}{d_o} + \frac{1}{d_i}$$

where $f$ – focal length, $d_o$ – object distance, $d_i$ – image distance.

Accordingly to the sign convention used here, for concave mirror $f$ should be positive, as well as $d_o$, while $d_i$ can change sign: “+” if image real (in front of the mirror) and “−” if image virtual (behind the mirror).

Then, for given case:

$$\frac{1}{f} = \frac{1}{10} - \frac{1}{5} = -\frac{1}{10} \rightarrow f = -10 < 0$$

Contradiction. Thus, there is no possible solution.

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