The objective lens of a compound microscope produces magnification of 10. In order to get an over all magnification of 100 when image is formed at 25 cm from the eye, the focal length of the eye lense should be (in cm)

Options

A. 4
B. 10
C. `25/9`
D. 9

Answer

To solve the problem step by step, we will use the information provided about the magnification of the objective lens and the overall magnification of the compound microscope.

### Step 1: Understand the given data
- Magnification of the objective lens (MO) = 10
- Overall magnification (m) = 100
- Least distance of distinct vision (D) = 25 cm

### Step 2: Write the formula for overall magnification
The overall magnification (m) of a compound microscope can be expressed as:
\[ m = MO \times \left(1 + \frac{D}{f_e}\right) \]
where \( f_e \) is the focal length of the eye lens.

### Step 3: Substitute the known values into the formula
Substituting the known values into the formula:
\[ 100 = 10 \times \left(1 + \frac{25}{f_e}\right) \]

### Step 4: Simplify the equation
Divide both sides by 10:
\[ 10 = 1 + \frac{25}{f_e} \]

### Step 5: Isolate the term involving \( f_e \)
Subtract 1 from both sides:
\[ 9 = \frac{25}{f_e} \]

### Step 6: Solve for \( f_e \)
Now, rearranging the equation to solve for \( f_e \):
\[ f_e = \frac{25}{9} \]

### Step 7: Calculate the value of \( f_e \)
Calculating the value:
\[ f_e \approx 2.77 \text{ cm} \]

### Final Answer
The focal length of the eye lens should be approximately \( 2.77 \) cm.

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