Question

If a concave mirror with a focal length of 10.0 cm creates a real image 30.0 cm away on its principal axis, how far from the mirror is the corresponding object?

Answer 1

+15.0 cm.

Explanation:

For this question, we need to use the mirror formula

• `\frac{1}{f} = 1/d_o + 1/d_i`.

What the problem gives us is: f = 10.0 cm, and `d_i` = +30.0 cm. We know that `d_i` is positive because it forms a real image. So we are solving for `d_o`. Isolating the unknown to its own side of the equation, in this case by subtracting `1/d_i` from both sides, will accomplish this.

• `\frac{1}{d_o} = \frac{1}{f} - 1/d_i`

• `1/d_o = 1/10 -1/30`. FInd a common denominator.

• `1/d_o = 3/30 - 1/30`

• `1/d_o = 2/30`. To find `d_o`, take the reciprocal.

• `d_o = 30/2 = +15.0 cm`

The same process can be used if you know the distance from the object to the vertex of the mirror, and are looking for `d_i`.