A converging lens of 2.5cm focal length is used as a simple microscope producing virtual image at 25cm from the eye. The position of the object from the lens is (nearly)

Options

A. 1 cm
B. 2 cm
C. 2.2 cm
D. 4 cm

Answer

To find the position of the object from the lens when using a converging lens as a simple microscope, we can use the lens formula:

\[ \frac{1}{f} = \frac{1}{v} - \frac{1}{u} \]

Where:
- \( f \) is the focal length of the lens,
- \( v \) is the image distance from the lens,
- \( u \) is the object distance from the lens.

### Step 1: Identify the given values
- Focal length, \( f = 2.5 \) cm
- Image distance, \( v = 25 \) cm (since the image is virtual, we take it as positive)

### Step 2: Rearrange the lens formula
We need to find \( u \), so we rearrange the lens formula:
\[ \frac{1}{u} = \frac{1}{v} - \frac{1}{f} \]

### Step 3: Substitute the known values into the formula
Substituting the values of \( v \) and \( f \):
\[ \frac{1}{u} = \frac{1}{25} - \frac{1}{2.5} \]

### Step 4: Calculate \( \frac{1}{f} \)
Calculate \( \frac{1}{2.5} \):
\[ \frac{1}{2.5} = \frac{10}{25} \]

### Step 5: Substitute back into the equation
Now substituting this back into the equation:
\[ \frac{1}{u} = \frac{1}{25} - \frac{10}{25} = \frac{1 - 10}{25} = \frac{-9}{25} \]

### Step 6: Solve for \( u \)
Taking the reciprocal to find \( u \):
\[ u = \frac{-25}{9} \text{ cm} \]

### Step 7: Calculate the numerical value
Calculating \( \frac{-25}{9} \):
\[ u \approx -2.78 \text{ cm} \]

### Conclusion
The object is placed approximately \( 2.78 \) cm to the left of the lens (the negative sign indicates that the object is on the same side as the incoming light).

### Final Answer
The position of the object from the lens is nearly \( 2.78 \) cm (to the left of the lens).

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