How far from a convex lens of focal length 20 cm would you place an object to get a real image enlarged three times ?

Options

A. 15.6 cm
B. 20.5 cm
C. 26.66 cm
D. 33.85 cm

Explanation

To solve the problem of how far from a convex lens of focal length 20 cm an object should be placed to get a real image enlarged three times, we can follow these steps:

### Step-by-Step Solution:

1. **Identify Given Values:**
- Focal length of the lens (F) = 20 cm
- Magnification (M) = 3 (since the image is enlarged three times)

2. **Understand the Magnification Formula:**
- The magnification (M) for a lens is given by the formula:
\[ M = \frac{V}{U} \]
Where:
- \( V \) = image distance
- \( U \) = object distance

3. **Express Image Distance in Terms of Object Distance:**
- Since the magnification is 3, we can express the image distance (V) in terms of the object distance (U):
\[ V = 3U \]

4. **Apply the Lens Formula:**
- The lens formula is given by:
\[ \frac{1}{F} = \frac{1}{V} - \frac{1}{U} \]
- Substitute \( V = 3U \) into the lens formula:
\[ \frac{1}{20} = \frac{1}{3U} - \frac{1}{U} \]

5. **Simplify the Equation:**
- Rewrite the right side:
\[ \frac{1}{20} = \frac{1 - 3}{3U} = \frac{-2}{3U} \]
- Rearranging gives:
\[ \frac{2}{3U} = \frac{1}{20} \]

6. **Cross-Multiply to Solve for U:**
- Cross-multiplying gives:
\[ 2 \cdot 20 = 3U \]
- Therefore:
\[ 40 = 3U \]
- Solving for \( U \):
\[ U = \frac{40}{3} \approx 13.33 \text{ cm} \]

7. **Calculate the Object Distance:**
- Since the object distance is taken as negative in lens conventions, we have:
\[ U = -\frac{40}{3} \approx -13.33 \text{ cm} \]

### Final Answer:
The object should be placed approximately **13.33 cm** from the convex lens to obtain a real image that is enlarged three times.