A reflecting type telescope has a large concave spherical mirror of radius of curvature `80 cm` as objective. What is the magnifying power of telescope if eye piece used has a focal length of `1.6 cm` ?

Options

A. 100
B. 50
C. 25
D. 5

Explanation

To find the magnifying power of a reflecting type telescope, we follow these steps:

### Step 1: Identify the given values
- Radius of curvature of the concave mirror (R) = 80 cm
- Focal length of the eyepiece (fE) = 1.6 cm

### Step 2: Calculate the focal length of the objective mirror
The focal length (fO) of a concave mirror is given by the formula:
\[ fO = \frac{R}{2} \]
Substituting the value of R:
\[ fO = \frac{80 \text{ cm}}{2} = 40 \text{ cm} \]

### Step 3: Use the formula for magnifying power
The magnifying power (M) of a telescope is given by the formula:
\[ M = \frac{fO}{fE} \]
Substituting the values of fO and fE:
\[ M = \frac{40 \text{ cm}}{1.6 \text{ cm}} \]

### Step 4: Calculate the magnifying power
Now, perform the division:
\[ M = 25 \]

### Conclusion
The magnifying power of the reflecting type telescope is:
\[ M = 25 \]

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