An object is 15.0 cm in front of a convex mirror. Its virtual image is 7.5 cm behind the mirror. Find focal length using real-is-positive mirror signs.

Solution & explanation

1. Define the convention: real object u is positive; virtual image v and convex-mirror focal length are negative.

2. Given: u = +15 cm; v = −7.5 cm.

3. Write the mirror equation.

   $$\frac{1}{f}=\frac{1}{v}+\frac{1}{u}$$

4. Insert signs before calculating.

   $$\frac{1}{f}=\frac{1}{-7.5}+\frac{1}{15}$$

5. Use a common denominator.

   $$\frac{1}{f}=-1\times \frac{2}{15}+\frac{1}{15}=-\frac{1}{15}$$

6. Take reciprocal of both sides.

   $$f=-15$$

7. State the result with units: f = −15 cm in the stated convention.

f = −15 cm