a 15.0 cm object is 12.0 cm from a concave mirror that has a focal length of 4.8 cm. its image is 8.0 cm in…

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 $h_o = 15.0$ cm, $d_o=12.0$ cm, and $d_i = 8.0$ cm.

Step3: Calculate magnification using distance ratio

First, calculate the magnification using the distance part of the formula: $m=-\frac{d_i}{d_o}=-\frac{8.0}{12.0}=-\frac{2}{3}$.

Step4: Solve for image height

Then, use the height - related part of the magnification formula $m=\frac{h_i}{h_o}$. Rearranging for $h_i$ gives $h_i=m\times h_o$. Substitute $m =-\frac{2}{3}$ and $h_o = 15.0$ cm into the formula: $h_i=-\frac{2}{3}\times15.0=- 10$ cm.

Answer:

-10 cm