#### Question

A convex mirror is needed to produce an image one-half the size of an object and located 36 cm behind the mirror. What focal length should the mirror have?

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#### Step 1

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In this problem, we have a convex mirror, where we need to find the focal length of the mirror. To solve this, we are going to use the mirror equation $\frac{1}{f} = \frac{1}{d_{o}}+ \frac{1}{d_{i}}$ where $f$ is the focal length of mirror, $d_{o}$ is the position of our object, and $d_{i}$ is the position of image. Also, we are going to use the magnification equation to find the image height $M= -\frac{d_{i}}{d_{o}}= \frac{h_{i}}{h_{o}}$

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