A convex lens of focal length f produces an image `1/n` times than that of the size of the object. The distance of the object from the lens is:

Options

A. nf
B. `f/n`
C. (n+1)f
D. (n-1)f

Answer

To solve the problem, we need to find the distance of the object from a convex lens given that the image produced is \( \frac{1}{n} \) times the size of the object.

### Step-by-Step Solution:

1. **Understand Magnification**:
The magnification \( m \) produced by a lens is given by the formula:
\[ m = \frac{v}{u} \]
where \( v \) is the image distance and \( u \) is the object distance. According to the problem, the magnification is \( \frac{1}{n} \), so we can write:
\[ \frac{v}{u} = \frac{1}{n} \]

2. **Express Image Distance**:
From the magnification equation, we can express \( v \) in terms of \( u \):
\[ v = \frac{u}{n} \]

3. **Use Lens Formula**:
The lens formula relates the focal length \( f \), image distance \( v \), and object distance \( u \):
\[ \frac{1}{f} = \frac{1}{v} - \frac{1}{u} \]
Substituting \( v = \frac{u}{n} \) into the lens formula gives:
\[ \frac{1}{f} = \frac{n}{u} - \frac{1}{u} \]
Simplifying this, we find:
\[ \frac{1}{f} = \frac{n - 1}{u} \]

4. **Rearranging for Object Distance**:
Rearranging the equation to solve for \( u \):
\[ u = f(n - 1) \]

5. **Conclusion**:
The distance of the object from the lens is:
\[ u = f(n - 1) \]

### Final Answer:
The distance of the object from the lens is \( u = f(n - 1) \).