The focal length of a simple convex lens used as a magnifier is 10 cm. For the image to be formed at a distance of distinct vision D = 25 cm, the object must be placed away from the lens nearly at a distance of

Options

A. (a)5 cm
B. (b)7 cm
C. (c)8 cm
D. (d)16 cm

Answer

To solve the problem, we need to determine the distance at which the object must be placed from a simple convex lens in order to form an image at a distance of distinct vision (D = 25 cm), given that the focal length (f) of the lens is 10 cm.

### Step-by-Step Solution:

1. **Identify Given Values:**
- Focal length of the lens, \( f = 10 \) cm
- Distance of distinct vision (image distance), \( v = 25 \) cm

2. **Use the Lens Formula:**
The lens formula relates the object distance (u), image distance (v), and focal length (f) of a lens:
\[ \frac{1}{f} = \frac{1}{v} + \frac{1}{u} \]

3. **Rearranging the Lens Formula:**
We can rearrange the formula to find \( u \):
\[ \frac{1}{u} = \frac{1}{f} - \frac{1}{v} \]

4. **Substituting the Known Values:**
Substitute \( f = 10 \) cm and \( v = 25 \) cm into the equation:
\[ \frac{1}{u} = \frac{1}{10} - \frac{1}{25} \]

5. **Finding a Common Denominator:**
The least common multiple of 10 and 25 is 50. So, we convert the fractions:
\[ \frac{1}{10} = \frac{5}{50}, \quad \frac{1}{25} = \frac{2}{50} \]
Thus,
\[ \frac{1}{u} = \frac{5}{50} - \frac{2}{50} = \frac{3}{50} \]

6. **Calculating \( u \):**
Now, we can find \( u \):
\[ u = \frac{50}{3} \approx 16.67 \text{ cm} \]

7. **Interpreting the Result:**
The object distance \( u \) is positive, indicating that the object is placed on the same side as the incoming light (which is the convention for a real object).

### Final Answer:
The object must be placed approximately at a distance of **16.67 cm** from the lens.