If we need a magnification of 400 from compound microscope of tube length 150 mm and an objective of focal length 5 mm, the focal length of the eye-piece, should be close to : (final Image is at infinity).

Options

A. 22mm
B. 19mm
C. 33mm
D. 2mm

Explanation

To solve the problem of finding the focal length of the eyepiece (FE) for a compound microscope with a given magnification, tube length, and objective focal length, we can follow these steps:

### Step 1: Understand the magnification formula
The total magnification (M) of a compound microscope is given by the formula:
\[ M = \frac{D}{f_o} \times \frac{L}{f_e} \]
where:
- \( D \) = near point distance (typically 25 cm or 250 mm)
- \( f_o \) = focal length of the objective
- \( L \) = tube length
- \( f_e \) = focal length of the eyepiece

### Step 2: Convert all measurements to the same unit
Given:
- \( M = 400 \)
- \( L = 150 \) mm
- \( f_o = 5 \) mm
- \( D = 250 \) mm (since 25 cm = 250 mm)

### Step 3: Substitute the known values into the magnification formula
Substituting the known values into the magnification formula:
\[ 400 = \frac{250}{5} \times \frac{150}{f_e} \]

### Step 4: Simplify the equation
First, calculate \( \frac{250}{5} \):
\[ \frac{250}{5} = 50 \]

Now substitute this back into the equation:
\[ 400 = 50 \times \frac{150}{f_e} \]

### Step 5: Rearrange to find \( f_e \)
Rearranging the equation to isolate \( f_e \):
\[ f_e = 50 \times \frac{150}{400} \]

### Step 6: Calculate the value of \( f_e \)
Now calculate \( f_e \):
\[ f_e = 50 \times \frac{150}{400} = 50 \times 0.375 = 18.75 \text{ mm} \]

### Step 7: Round to the nearest value
Since the question asks for the focal length to be close to a specific value, we can round \( 18.75 \) mm to \( 19 \) mm.

### Final Answer
The focal length of the eyepiece should be close to **19 mm**.

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