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 then"`(d)/(4)`

Answer

To solve the problem, we need to determine the required focal length of a convex lens that produces an image of equal size to the object when the lens is placed at a distance \( d \) ahead of the second wall.

### Step-by-Step Solution:

1. **Understanding the Setup:**
- We have two parallel walls.
- A convex lens is placed between these walls.
- The distance between the two walls is \( D \).
- The lens is placed at a distance \( d \) from the second wall.

2. **Image Formation by a Convex Lens:**
- For a convex lens, the image formed is of the same size as the object when the object is placed at a distance of \( 2f \) from the lens, where \( f \) is the focal length of the lens.
- The image will also be formed at a distance of \( 2f \) on the opposite side of the lens.

3. **Relating Distances:**
- The total distance between the object and the image is \( D \).
- Since the lens is \( d \) away from the second wall, the distance from the lens to the first wall (where the object is located) is \( D - d \).

4. **Setting Up the Equation:**
- For the image to be of equal size as the object, the distance from the object to the lens must be \( 2f \), and the distance from the lens to the image must also be \( 2f \).
- Therefore, we can write the equation:
\[ (D - d) + d = 4f \]
- This simplifies to:
\[ D = 4f \]

5. **Finding the Focal Length:**
- Rearranging the equation gives us:
\[ f = \frac{D}{4} \]
- However, since we need to express \( f \) in terms of \( d \), we know that \( D = d + 2f \) (the total distance from the object to the image).
- Substituting \( D \) into the equation gives:
\[ d + 2f = 4f \]
- Rearranging gives:
\[ d = 4f - 2f = 2f \]
- Thus, we find:
\[ f = \frac{d}{2} \]

### Final Answer:
The required focal length \( f \) of the lens is:
\[ f = \frac{d}{2} \]