To solve for the height of the image and determine the type of mirror, we need to follow these steps:
### Step 1: Find the Magnification
The magnification ([tex]\(m\)[/tex]) is given by the formula:
[tex]\[
m = -\frac{\text{distance of image}}{\text{distance of object}}
\][/tex]
Given:
- Distance of the image ([tex]\(d_i\)[/tex]) = -21 cm
- Distance of the object ([tex]\(d_o\)[/tex]) = 8 cm
Substituting these values into the formula:
[tex]\[
m = -\frac{-21}{8} = \frac{21}{8} = 2.625
\][/tex]
### Step 2: Calculate the Height of the Image
The height of the image ([tex]\(h_i\)[/tex]) can be found using the magnification formula related to height:
[tex]\[
h_i = m \times \text{height of object}
\][/tex]
Given the height of the object is 4 cm,
[tex]\[
h_i = 2.625 \times 4 = 10.5 \, \text{cm}
\][/tex]
### Step 3: Round the Height of the Image
Rounding to the nearest whole number,
[tex]\[
h_i \approx 10 \, \text{cm}
\][/tex]
### Step 4: Determine the Type of Mirror
The sign of the image distance ([tex]\(d_i\)[/tex]) tells us about the type of mirror.
- If [tex]\(d_i\)[/tex] is negative, the image is formed on the same side as the object in concave mirrors.
Given that [tex]\(d_i = -21 \, \text{cm}\)[/tex], the image distance is negative, which indicates that the mirror is concave.
### Final Answer
1. The height of the image is approximately [tex]\( \boxed{10} \, \text{cm} \)[/tex].
2. The type of mirror most likely formed this image is [tex]\( \boxed{\text{concave}} \)[/tex].
