For compound microscope,`f_0=1` cm, `f-e=2.5cm`. An objects is placed at distance 1.2 cm from objects lens. What should be the length of microscope for normal adjustment?

Options

A. 8.5 cm
B. 8.3 cm
C. 6.5 cm
D. 6.3 cm

Answer

To find the length of the compound microscope for normal adjustment, we need to follow these steps:

### Step 1: Understand the given values
- Focal length of the objective lens, \( f_o = 1 \, \text{cm} \)
- Focal length of the eyepiece, \( f_e = 2.5 \, \text{cm} \)
- Object distance from the objective lens, \( u = -1.2 \, \text{cm} \) (the negative sign indicates that the object is placed on the same side as the incoming light)

### Step 2: Calculate the image distance from the objective lens
Using the lens formula for the objective lens:
\[ \frac{1}{f_o} = \frac{1}{v_o} - \frac{1}{u} \]
Where:
- \( v_o \) = image distance from the objective lens

Rearranging gives:
\[ \frac{1}{v_o} = \frac{1}{f_o} + \frac{1}{u} \]
Substituting the known values:
\[ \frac{1}{v_o} = \frac{1}{1} + \frac{1}{-1.2} \]
Calculating:
\[ \frac{1}{v_o} = 1 - \frac{5}{6} = \frac{1}{6} \]
Thus:
\[ v_o = 6 \, \text{cm} \]

### Step 3: Calculate the length of the microscope for normal adjustment
The total length of the microscope \( L \) in normal adjustment is given by:
\[ L = v_o + f_e \]
Substituting the values we have:
\[ L = 6 + 2.5 = 8.5 \, \text{cm} \]

### Final Answer
The length of the microscope for normal adjustment is \( 8.5 \, \text{cm} \).

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