Question

a 5.0 cm object is 12.0 cm from a concave mirror that has a focal length of 24.0 cm. the distance between the image and the mirror is cm.

Explanation:

Step1: Recall the mirror formula

The mirror formula is \(\frac{1}{f}=\frac{1}{u}+\frac{1}{v}\), where \(f\) is the focal length, \(u\) is the object distance, and \(v\) is the image distance.

Step2: Substitute the given values

Given \(f = 24.0\space cm\) and \(u=12.0\space cm\). Substitute into the formula: \(\frac{1}{24}=\frac{1}{12}+\frac{1}{v}\).

Step3: Solve for \(v\)

First, rewrite the equation as \(\frac{1}{v}=\frac{1}{24}-\frac{1}{12}\). Then \(\frac{1}{v}=\frac{1 - 2}{24}=-\frac{1}{24}\). So \(v=-24.0\space cm\).

Answer:

$-24.0$