# If an object is placed 25.0 cm from a concave mirror whose focal length is 5.0 cm, where is the image located?

Apr 30, 2014

For this question, we need to use the mirror formula $\frac{1}{f} = \frac{1}{d} _ o + \frac{1}{d} _ i$.

What the problem gives us is: f = 5.0 cm, and ${d}_{o}$ = 25.0 cm. So we are solving for ${d}_{i}$. Isolating the unknown to its own side of the equation, in this case by subtracting $\frac{1}{d} _ i$ from both sides, will accomplish this.

1/d_i = 1/f − 1/d_o

1/d_i = 1/5 − 1/25. FInd a common denominator.

1/d_i = 5/25 − 1/25

$\frac{1}{d} _ i = \frac{4}{25}$. To find ${d}_{i}$, take the reciprocal.

${d}_{i} = \frac{25}{4} = + 6.25 c m$

We know that this is a real image because ${d}_{i}$ is positive.

The same process can be used if you know the distance from the image to the vertex of the mirror, and are looking for ${d}_{o}$.