Magnification of a compound microscope is 30. Focal length of eye`-` piece is `5 cm` and the image is formed at a distance of distinct vision of `25 cm`. The magnificatio of the objective lens is

Options

A. 6
B. 5
C. 7.5
D. 10

Answer

To solve the problem of finding the magnification of the objective lens in a compound microscope, we can follow these steps:

### Step 1: Understand the given information
- Magnification of the compound microscope (M) = 30
- Focal length of the eyepiece (f_e) = 5 cm
- Distance of distinct vision (D) = 25 cm

### Step 2: Write the formula for the total magnification of a compound microscope
The total magnification (M) of a compound microscope is given by the product of the magnification of the objective lens (M_o) and the magnification of the eyepiece (M_e):
\[ M = M_o \times M_e \]

### Step 3: Calculate the magnification of the eyepiece (M_e)
The magnification of the eyepiece can be calculated using the formula:
\[ M_e = 1 + \frac{D}{f_e} \]
Substituting the known values:
\[ M_e = 1 + \frac{25 \, \text{cm}}{5 \, \text{cm}} \]
\[ M_e = 1 + 5 = 6 \]

### Step 4: Substitute the values to find the magnification of the objective lens (M_o)
Now, we can substitute the values of M and M_e into the first equation to find M_o:
\[ M_o = \frac{M}{M_e} \]
Substituting the known values:
\[ M_o = \frac{30}{6} \]
\[ M_o = 5 \]

### Conclusion
The magnification of the objective lens is 5.