Magnifying power of a simple microscope A is 1.25 less than that of a simple microscope B. If the power of the lens used in B is 25 D, find the power of lens used in A. Given that distance of distinct vision is 25 cm.

Answer

To solve the problem, we need to find the power of the lens used in microscope A, given that the magnifying power of microscope A is 1.25 less than that of microscope B, and the power of the lens used in microscope B is 25 D.

### Step-by-step Solution:

1. **Understanding Magnifying Power**:
The magnifying power (M) of a simple microscope is given by the formula:
\[ M = 1 + \frac{D}{F} \]
where D is the distance of distinct vision (25 cm or 0.25 m) and F is the focal length of the lens.

2. **Calculate the Focal Length of Microscope B**:
The power (P) of the lens is related to the focal length (F) by the formula:
\[ P = \frac{1}{F} \quad \text{(in meters)} \]
For microscope B, the power is given as 25 D. Therefore:
\[ F_B = \frac{1}{P_B} = \frac{1}{25} \text{ m} = 0.04 \text{ m} = 4 \text{ cm} \]

3. **Calculate the Magnifying Power of Microscope B**:
Now we can calculate the magnifying power of microscope B:
\[ M_B = 1 + \frac{D}{F_B} = 1 + \frac{25 \text{ cm}}{4 \text{ cm}} = 1 + 6.25 = 7.25 \]

4. **Determine the Magnifying Power of Microscope A**:
According to the problem, the magnifying power of microscope A is 1.25 less than that of microscope B:
\[ M_A = M_B - 1.25 = 7.25 - 1.25 = 6 \]

5. **Set Up the Equation for Microscope A**:
Using the magnifying power formula for microscope A:
\[ M_A = 1 + \frac{D}{F_A} \]
Substituting the known values:
\[ 6 = 1 + \frac{25 \text{ cm}}{F_A} \]

6. **Solve for Focal Length of Microscope A**:
Rearranging the equation gives:
\[ 6 - 1 = \frac{25 \text{ cm}}{F_A} \implies 5 = \frac{25 \text{ cm}}{F_A} \]
Thus,
\[ F_A = \frac{25 \text{ cm}}{5} = 5 \text{ cm} \]

7. **Calculate the Power of Lens Used in Microscope A**:
Now we can find the power of the lens used in microscope A:
\[ P_A = \frac{1}{F_A} = \frac{1}{0.05 \text{ m}} = 20 \text{ D} \]

### Final Answer:
The power of the lens used in microscope A is **20 D**.