The length of the tube of a microscope is 10 cm . The focal lengths of the objective and eye lenses are 0.5 cm and 1.0 cm . The magnifying power of the microscope is about

Options

A. 5
B. 23
C. 166
D. 500

Explanation

To find the magnifying power of the microscope, we can use the formula for magnifying power (M) given by:

\[ M = \frac{V_o}{U_o} \times \frac{D}{f_e} \]

Where:
- \( V_o \) = distance of the image formed by the objective lens
- \( U_o \) = distance of the object from the objective lens
- \( D \) = least distance of distinct vision (typically taken as 25 cm)
- \( f_e \) = focal length of the eye lens

### Step 1: Identify the given values
- Length of the tube (L) = 10 cm
- Focal length of the objective lens (\( f_o \)) = 0.5 cm
- Focal length of the eye lens (\( f_e \)) = 1.0 cm
- Least distance of distinct vision (D) = 25 cm

### Step 2: Assume the object is placed at the focus of the objective lens
Since the object is placed at the focus of the objective lens, we can set:
- \( U_o = f_o = 0.5 \) cm

### Step 3: Calculate the distance of the image formed by the objective lens
The image distance \( V_o \) can be assumed to be equal to the length of the tube, which is:
- \( V_o = L = 10 \) cm

### Step 4: Substitute the values into the magnifying power formula
Now, substituting the values into the magnifying power formula:

\[ M = \frac{V_o}{U_o} \times \frac{D}{f_e} \]

Substituting the known values:

\[ M = \frac{10 \, \text{cm}}{0.5 \, \text{cm}} \times \frac{25 \, \text{cm}}{1 \, \text{cm}} \]

### Step 5: Calculate the magnifying power
Calculating the first part:

\[ \frac{10}{0.5} = 20 \]

Now calculating the second part:

\[ \frac{25}{1} = 25 \]

Now multiply these two results:

\[ M = 20 \times 25 = 500 \]

### Final Result
The magnifying power of the microscope is approximately 500.

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