A magnifying glass is made of a combination of a convergent lens of power 20D and and divergent lens of power 4D. If the least distance of distinct vision is 25cm. The magnifying power is

Options

A. 7
B. 5
C. 3
D. 8

Answer

To solve the problem step by step, we will follow the given information about the convergent and divergent lenses, calculate the power of the combination, find the focal length, and then determine the magnifying power.

### Step 1: Identify the powers of the lenses
- The power of the convergent lens (P_c) is given as +20 D (diopters).
- The power of the divergent lens (P_d) is given as -4 D (since the power of a divergent lens is negative).

### Step 2: Calculate the total power of the combination
The total power (P) of the combination of the two lenses is calculated using the formula:
\[ P = P_c + P_d \]
Substituting the values:
\[ P = 20 D + (-4 D) = 20 D - 4 D = 16 D \]

### Step 3: Calculate the focal length of the combination
The focal length (f) of the combination can be found using the formula:
\[ f = \frac{1}{P} \]
Substituting the power we found:
\[ f = \frac{1}{16 D} \]
Since 1 D = 1 m⁻¹, we have:
\[ f = \frac{1}{16} \text{ m} = 0.0625 \text{ m} \]

### Step 4: Convert the focal length to centimeters
To convert the focal length from meters to centimeters:
\[ f = 0.0625 \text{ m} \times 100 \text{ cm/m} = 6.25 \text{ cm} \]

### Step 5: Calculate the magnifying power
The magnifying power (M) of the magnifying glass is given by the formula:
\[ M = 1 + \frac{D}{f} \]
Where D is the least distance of distinct vision (25 cm). Substituting the values:
\[ M = 1 + \frac{25 \text{ cm}}{6.25 \text{ cm}} \]
Calculating the division:
\[ M = 1 + 4 = 5 \]

### Final Answer
The magnifying power of the magnifying glass is **5**.

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