Question

an object of height 4.62 cm is placed 27.1 cm from a concave mirror. the image is 11.5 cm from the mirror. how tall is the image? ? cm

Explanation:

Step1: Recall magnification formula

The magnification \( m \) of a mirror is given by two equivalent expressions:
$$m = -\frac{d_i}{d_o} = \frac{h_i}{h_o}$$
where \( d_o = 27.1\ \text{cm} \) (object distance), \( d_i = 11.5\ \text{cm} \) (image distance), \( h_o = 4.62\ \text{cm} \) (object height), and \( h_i \) is the image height we need to find.

Step2: Isolate image height term

Rearrange the formula to solve for \( h_i \):
$$h_i = -\frac{d_i}{d_o} \times h_o$$

Step3: Substitute given values

Plug in the known values:
$$h_i = -\frac{11.5}{27.1} \times 4.62$$

Step4: Calculate the result

First compute \( \frac{11.5}{27.1} \approx 0.42435 \), then multiply by 4.62:
$$h_i \approx -0.42435 \times 4.62 \approx -1.93\ \text{cm}$$
The negative sign indicates the image is inverted, so the magnitude of the image height is 1.93 cm.

Answer:

1.93 cm