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Chapter 31: Problem 39

An object's image in a 27 -cm-focal-length concave mirror is upright and magnified by a factor of \(3 .\) Where is the object?

Short Answer

Expert verified
The object is located 36 cm in front of the mirror.

Step by step solution

01

Understanding the Problem Variables

We are given the mirror's focal length \(f = -27 cm\) (negative because it is a concave mirror). We also know the magnification \(m = 3\) (upright image). We are to find the object's location \(p\).
02

Using the magnification formula

Magnification for mirrors equals the focal length divided by the focal length minus the object distance (\(m = f / (f - p)\)). We can re-arrange this formula to solve for \(p\) using the known values of \(m\) and \(f\), thus getting the equation \(p = f / m + f\). Using the above formula, when \(m = 3\) and \(f = -27 cm\), the object position \(p = -27 cm / 3 + -27 cm = -27 cm + -9 cm = -36 cm \).
03

Interpreting the result

The negative result implies that the object is positioned on the same side of the mirror as the light being reflected (real object), which is standard for mirrors. The object is 36 cm away from the mirror.

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