**Given information:**

- Two identical thin converging lenses are brought in contact so that their axes coincide.
- The lenses are placed 12.5 cm from an object.
- The size of the real image formed by the system of lenses is four times as large as the object.

**To find:**
- The optical power of the system of lenses.
- The optical power of each lens.
- Explanation in detail.

**Solution:**

**1. Optical Power of the System of Lenses:**
The optical power of a lens is given by the formula:

Optical Power (P) = 1 / F

Where F is the focal length of the lens.

Since two identical lenses are brought in contact, their focal lengths add up. Let's assume the focal length of each lens is f.
Therefore, the total focal length of the system of lenses (F_total) is:

F_total = f + f = 2f

The optical power of the system of lenses (P_total) is:

P_total = 1 / F_total = 1 / (2f)

**2. Optical Power of Each Lens:**
Since the two lenses are identical, their optical powers will be the same. Let's assume the optical power of each lens is P.

P = P_total (since both lenses are identical)

Therefore, the optical power of each lens is:

P = 1 / (2f)

**3. Magnification of the System of Lenses:**
The magnification (M) of the system of lenses is given by the formula:

M = -v / u

Where v is the image distance and u is the object distance.

Given that the size of the real image formed by the system of lenses is four times as large as the object, we can write:

M = v / u = 4

**4. Relationship between Object Distance, Image Distance, and Focal Length:**
For a thin converging lens, the relationship between the object distance (u), image distance (v), and focal length (f) is given by the lens formula:

1 / f = 1 / v - 1 / u

Since the lenses are placed in contact, the object distance for the second lens will be the image distance of the first lens. Therefore, we can write:

u = v

Substituting this in the lens formula, we get:

1 / f = 1 / v - 1 / u = 1 / v - 1 / v = 0

This implies that the focal length of each lens is infinity, which means the lenses are acting as a converging lens with no focal length.

**Conclusion:**
- The optical power of the system of lenses is 1 / (2f).
- The optical power of each lens is 1 / (2f).
- The focal length of each lens is infinity.
- The size of the real image formed by the system of lenses is four times as large as the object.