An opera glass `(`Galilean telescope ) measures `9cm` from the objective to the eyepiece. The focal length of the objective is `15 cm`. Its magnifying power is

Options

A. 2.5
B. `2/5`
C. `5/3`
D. 0.4

Explanation

To find the magnifying power of the Galilean telescope (opera glass), we can follow these steps:

### Step 1: Understand the relationship between the focal lengths and the length of the telescope
For a Galilean telescope, the distance \( L \) between the objective and the eyepiece is given by the formula:
\[ L = F_o + F_e \]
where \( F_o \) is the focal length of the objective lens and \( F_e \) is the focal length of the eyepiece lens.

### Step 2: Substitute the known values
From the problem, we know:
- The total length \( L = 9 \, \text{cm} \)
- The focal length of the objective \( F_o = 15 \, \text{cm} \)

We can substitute these values into the equation:
\[ 9 = 15 + F_e \]

### Step 3: Solve for the focal length of the eyepiece
Rearranging the equation to find \( F_e \):
\[ F_e = 9 - 15 = -6 \, \text{cm} \]
The negative sign indicates that the eyepiece is a diverging lens.

### Step 4: Calculate the magnifying power
The magnifying power \( M \) of a Galilean telescope is given by the formula:
\[ M = \frac{F_o}{|F_e|} \]
Substituting the values we have:
\[ M = \frac{15 \, \text{cm}}{6 \, \text{cm}} = 2.5 \]

### Step 5: Conclusion
Thus, the magnifying power of the Galilean telescope is:
\[ M = 2.5 \]