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…

Answer:

$-3.2$

Explanation:

Step1: Recall magnification formula

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

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: First find the magnification using distance

$m=-\frac{d_i}{d_o}=-\frac{16.0}{40.0}=- 0.4$

Step4: Then find the image height

Since $m=\frac{h_i}{h_o}$, we can solve for $h_i$. Rearranging gives $h_i=m\times h_o$. Substituting $m = - 0.4$ and $h_o = 8.0$ cm, we get $h_i=-0.4\times8.0=-3.2$ cm. The negative sign indicates that the image is inverted. So the height of the image to the nearest tenth is $3.2$ cm.