an 8.0 cm object is 40.0 cm from a concave mirror that has a focal length of 10.0 cm. its image is 16.0 cm…

Explanation:

Step1: Recall magnification formula

The magnification formula for mirrors is $m =-\frac{d_i}{d_o}=\frac{h_i}{h_o}$, where $d_i$ is the image - distance, $d_o$ is the object - distance, $h_i$ is the height of the image, and $h_o$ is the height of the object.

Step2: Identify given values

We are given that $d_o = 40.0$ cm, $d_i=16.0$ cm, and $h_o = 8.0$ cm.

Step3: Substitute values into magnification formula

First, from $-\frac{d_i}{d_o}=\frac{h_i}{h_o}$, we can solve for $h_i$. Cross - multiply to get $h_i=-\frac{d_i}{d_o}\times h_o$. Substitute $d_i = 16.0$ cm, $d_o = 40.0$ cm, and $h_o = 8.0$ cm into the formula: $h_i=-\frac{16.0}{40.0}\times8.0$. $h_i=- 3.2$ cm. The negative sign indicates that the image is inverted. The magnitude of the height is what we are interested in for the physical size.

Answer:

3.2