To understand why the correct answer is option 'C', let's break down the concept step by step.

1. Virtual Image:
When an object is placed in front of a concave mirror, a virtual image is formed. A virtual image is an image that cannot be projected onto a screen. It is formed by the apparent intersection of light rays that appear to come from a point behind the mirror.

2. Magnification:
The magnification of an image is the ratio of the height of the image to the height of the object. It determines how much larger or smaller the image appears compared to the object. Mathematically, magnification (m) is given by the formula:

m = -v/u

where v is the image distance (distance of the image from the mirror) and u is the object distance (distance of the object from the mirror).

In this case, the magnification is given as 2, which means the image height is twice the object height.

3. Real Image:
A real image is formed when the light rays actually converge and can be projected onto a screen. It is formed when the object is placed beyond the focal point of the mirror.

4. Relationship between Magnification and Object Distance:
The magnification of a real image formed by a concave mirror is positive. This means that the object distance (u) and the image distance (v) have the same sign. In this case, since the magnification is given as 2, the object distance and the image distance are both positive or both negative.

5. Relationship between Object Distance and Image Distance:
The relationship between the object distance (u), image distance (v), and focal length (f) of a concave mirror is given by the mirror formula:

1/f = 1/v - 1/u

In this case, we want to find the object distance (u) for a real image with a magnification of 2.

6. Applying the Given Conditions:
Given that the magnification is 2, we can substitute the values into the magnification formula:

2 = v/u

Since the magnification is positive for a real image, both v and u have the same sign. Let's assume they are positive.

7. Calculating the Object Distance:
Now, substitute the magnification formula into the mirror formula:

1/f = 1/v - 1/u

1/f = 1/u - 1/u

1/f = 0

This implies that the focal length is infinity, which is not possible for a concave mirror. Therefore, the assumption that both v and u are positive is incorrect.

8. Correcting the Assumption:
Let's assume that both v and u are negative. Now, substitute the magnification formula into the mirror formula:

1/f = 1/v - 1/u

1/f = 1/(-2u) - 1/u

1/f = -1/u

This implies that u = -f.

9. Finding the Required Object Distance:
To obtain a real image with a magnification of 2, we need to find the change in object distance (Δu) by subtracting the initial object distance (u) from the new object distance (u').

Δu = u' - u

Since u = -f and u' = -2f (as magnification is 2), we have:

Δu = -2f - (-f)