A convex lens of focal length 10 cm and imag formed by it, is at least distance of distinct vision then the magnifying power is

Options

A. 3.5
B. 2.5
C. 1.5
D. 1.4

Answer

To solve the problem step by step, we will use the lens formula and the magnifying power formula for a convex lens.

### Step 1: Understand the Given Information
- Focal length of the convex lens (f) = 10 cm
- The image is formed at the least distance of distinct vision (D) = 25 cm

### Step 2: Set Up the Lens Formula
The lens formula is given by:
\[ \frac{1}{f} = \frac{1}{v} - \frac{1}{u} \]
Where:
- \( f \) = focal length of the lens
- \( v \) = image distance (positive for real images, negative for virtual images)
- \( u \) = object distance (negative for real objects)

Since the image is formed at the least distance of distinct vision, we take:
\[ v = -25 \text{ cm} \quad (\text{negative because the image is virtual}) \]

### Step 3: Substitute Known Values into the Lens Formula
Substituting the known values into the lens formula:
\[ \frac{1}{10} = \frac{1}{-25} - \frac{1}{u} \]

### Step 4: Rearrange the Equation to Solve for \( u \)
Rearranging the equation gives:
\[ \frac{1}{u} = \frac{1}{-25} - \frac{1}{10} \]
Finding a common denominator (which is 50):
\[ \frac{1}{u} = \frac{-2}{50} - \frac{5}{50} = \frac{-7}{50} \]
Thus,
\[ u = -\frac{50}{7} \text{ cm} \]

### Step 5: Calculate the Magnifying Power
The magnifying power (M) of a lens is given by:
\[ M = \frac{v}{u} \]
Substituting the values we found:
\[ M = \frac{-25}{-\frac{50}{7}} = \frac{25 \cdot 7}{50} = \frac{175}{50} = \frac{7}{2} = 3.5 \]

### Final Answer
The magnifying power of the convex lens is **3.5**.

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