An object is gradually moving away from the focal point of a converging lens along the axis of the lens. The graphical representation of the magnitude of linear magnification (m) versus distance of the object from the lens (x) is correctly given by : (Graphs are drawn schematically and are not to scale)

Options

A.
B.
C.
D.

Explanation

To solve the problem of determining the correct graphical representation of the magnitude of linear magnification (m) versus the distance of the object from the lens (x) for a converging lens, we can follow these steps:

### Step 1: Understand the Lens Formula
The lens formula is given by:
\[ \frac{1}{v} - \frac{1}{u} = \frac{1}{f} \]
Where:
- \( v \) is the image distance,
- \( u \) is the object distance (negative for real objects),
- \( f \) is the focal length (positive for converging lenses).

### Step 2: Express Image Distance in Terms of Object Distance
From the lens formula, we can rearrange it to find the image distance \( v \):
\[ v = \frac{uf}{u + f} \]

### Step 3: Determine the Magnification
The magnification \( m \) is defined as:
\[ m = \frac{v}{u} \]
Substituting the expression for \( v \):
\[ m = \frac{uf}{u + f} \cdot \frac{1}{u} = \frac{f}{u + f} \]

### Step 4: Analyze the Behavior of Magnification
As the object distance \( u \) increases (the object moves away from the lens):
- When \( u \) approaches infinity, \( m \) approaches 0.
- When \( u \) is equal to \( f \) (the focal length), \( m \) is 1.
- As \( u \) decreases towards \( f \), the magnification increases.

### Step 5: Graphical Representation
The relationship between the magnitude of magnification \( |m| \) and the object distance \( |u| \) can be summarized:
- At \( u = f \), \( |m| = 1 \).
- As \( u \) increases beyond \( f \), \( |m| \) decreases towards 0.
- The graph will show a decreasing curve starting from \( |m| = 1 \) and approaching \( |m| = 0 \) as \( u \) increases.

### Conclusion
The correct graphical representation of the magnitude of linear magnification versus the distance of the object from the lens is a curve that starts at \( |m| = 1 \) when \( u = f \) and decreases towards 0 as \( u \) approaches infinity. Therefore, the correct option is represented by curve B.

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