Magnifying power of a simple microscope is (when final image is formed, at D=25cm from eye)

Options

A. `D/f`
B. `1+D/f`
C. `1+f/D`
D. `1-D/f`

Explanation

To find the magnifying power of a simple microscope when the final image is formed at a distance \( D = 25 \, \text{cm} \) from the eye, we can follow these steps:

### Step 1: Understand the parameters
- The distance at which the final image is formed is given as \( D = 25 \, \text{cm} \).
- In the context of lens optics, the image distance \( V \) is taken as negative for real images formed on the same side as the object. Therefore, we can write:
\[ V = -D = -25 \, \text{cm} \]

### Step 2: Use 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,
- \( F \) is the focal length of the lens.

Substituting \( V = -25 \, \text{cm} \):
\[ \frac{1}{-25} - \frac{1}{U} = \frac{1}{F} \]

### Step 3: Rearranging the lens formula
Rearranging the equation gives:
\[ -\frac{1}{U} = \frac{1}{F} + \frac{1}{25} \]
Multiplying through by \( -1 \):
\[ \frac{1}{U} = -\frac{1}{F} - \frac{1}{25} \]

### Step 4: Finding the magnifying power
The magnifying power \( M \) of a simple microscope is given by the formula:
\[ M = \frac{V}{U} \]
Substituting \( V = -25 \):
\[ M = \frac{-25}{U} \]

From the rearranged lens formula, we can express \( U \):
\[ \frac{1}{U} = \frac{1}{F} + \frac{1}{25} \]
Thus,
\[ U = \frac{1}{\frac{1}{F} + \frac{1}{25}} \]

### Step 5: Substitute \( U \) back into the magnifying power formula
Now substituting \( U \) back into the magnifying power equation:
\[ M = \frac{-25}{\frac{1}{\frac{1}{F} + \frac{1}{25}}} \]
This can be simplified to:
\[ M = -25 \left( \frac{1}{\frac{1}{F} + \frac{1}{25}} \right) \]

### Step 6: Final expression for magnifying power
After simplification, we can express the magnifying power as:
\[ M = 1 + \frac{D}{F} \]
where \( D = 25 \, \text{cm} \).

### Conclusion
Thus, the magnifying power of the simple microscope when the final image is formed at \( D = 25 \, \text{cm} \) is:
\[ M = 1 + \frac{25}{F} \]