A philatelist examines the printing details on a stamp using a convex lens of focal length 10.0 cm as a simple magnifier. The lens is held close to the eye and the lens to object distance is adjusted so that the virtual image is formed at the normal near point (25 cm). Calculate magnification.

Answer

To solve the problem step by step, we will use the lens formula and the formula for magnification.

### Step 1: Understand the given information
- Focal length of the convex lens (f) = 10.0 cm
- The virtual image is formed at the near point (d) = 25.0 cm

### Step 2: Write the formula for magnification
The magnification (m) produced by a lens is given by:
\[ m = \frac{V}{u} \]
where:
- V = image distance
- u = object distance

### Step 3: Use the lens formula
The lens formula is given by:
\[ \frac{1}{f} = \frac{1}{v} - \frac{1}{u} \]
Rearranging this, we can express it in terms of V:
\[ \frac{V}{f} = 1 - \frac{V}{u} \]

### Step 4: Substitute magnification into the lens formula
From the magnification formula, we know that:
\[ m = \frac{V}{u} \]
Thus, we can substitute \( \frac{V}{u} \) with m in the lens formula:
\[ \frac{V}{f} = 1 - m \]

### Step 5: Rearranging to find magnification
From the above equation, we can express m as:
\[ m = 1 - \frac{V}{f} \]
Since V is the distance at which the virtual image is formed (25 cm), we substitute V and f:
\[ m = 1 - \frac{25}{10} \]
\[ m = 1 - 2.5 \]
\[ m = 1 + \frac{25}{10} \]
\[ m = 1 + 2.5 \]
\[ m = 3.5 \]

### Step 6: Conclusion
The magnification produced by the convex lens is:
\[ m = 3.5 \]