A concave mirror is used to focus the image of a flower on a nearby well 120 cm from the flower. If a lateral magnification of 16 is desired, the distance of the flower from the mirror should be

Options

A. 8 cm
B. 12 cm
C. 80 cm
D. 120 cm

Answer

To solve the problem, we will use the mirror formula and the magnification formula for a concave mirror.

### Step-by-Step Solution:

1. **Identify the Given Values:**
- The distance from the flower to the well (image distance, \( v \)) = 120 cm
- Lateral magnification (\( m \)) = 16

2. **Understand the Sign Convention:**
- For a concave mirror, the object distance (\( u \)) is taken as negative.
- The image distance (\( v \)) is positive since the image is formed on the same side as the object (real image).

3. **Use the Magnification Formula:**
The magnification (\( m \)) for mirrors is given by:
\[ m = -\frac{v}{u} \]
Substituting the known values:
\[ 16 = -\frac{120 + u}{u} \]
Here, \( v \) is expressed as \( 120 + u \) because the image distance is measured from the mirror to the well, which is \( 120 \) cm plus the object distance \( u \).

4. **Rearranging the Equation:**
Multiply both sides by \( u \):
\[ 16u = -(120 + u) \]
Rearranging gives:
\[ 16u + u = -120 \]
\[ 17u = -120 \]

5. **Solving for \( u \):**
\[ u = -\frac{120}{17} \approx -7.06 \text{ cm} \]
Since \( u \) is negative, it indicates that the flower is located 7.06 cm in front of the mirror.

6. **Final Answer:**
The distance of the flower from the mirror is approximately \( 7.06 \) cm.