A body is located on a wall. Its image of equal size is to be obtained on a parallel wall with the help of a convex leng. The lens is placed at a distance d ahead of second wall, then the required focal length will be:

Options

A. Only `(d)/(4)`
B. Only `(d)/(2)`
C. More than `(d)/(4)` but less than `(d)/(2)`
D. Less than `(d)/(4)`

Explanation

To solve the problem step by step, we will analyze the situation described and apply the lens formula and magnification concepts.

### Step-by-Step Solution:

1. **Understanding the Setup**:
- We have a body located on one wall and we want to form an image of this body on a parallel wall using a convex lens.
- The image formed should be of equal size to the object.

2. **Identifying Distances**:
- Let the distance between the lens and the second wall (where the image is to be formed) be \( d \).
- Since the image is to be of equal size as the object, we denote the object distance \( u \) and the image distance \( v \).
- Given that the image is formed at distance \( d \), we have \( v = d \).

3. **Using Magnification**:
- The magnification \( m \) is given by the formula:
\[ m = \frac{V}{U} \]
- Since the image is of equal size to the object, we have \( m = 1 \). Therefore:
\[ \frac{d}{u} = 1 \implies u = d \]

4. **Applying the Lens Formula**:
- The lens formula is given by:
\[ \frac{1}{f} = \frac{1}{v} - \frac{1}{u} \]
- Substituting the values of \( v \) and \( u \):
\[ \frac{1}{f} = \frac{1}{d} - \frac{1}{(-d)} \]
- Here, \( u \) is negative because the object is on the opposite side of the lens.

5. **Simplifying the Equation**:
- The equation becomes:
\[ \frac{1}{f} = \frac{1}{d} + \frac{1}{d} = \frac{2}{d} \]
- Therefore, we can find \( f \):
\[ f = \frac{d}{2} \]

6. **Conclusion**:
- The required focal length \( f \) of the convex lens to obtain an image of equal size on the parallel wall is:
\[ f = \frac{d}{2} \]