An astronomical telescope has objective and eye-piece lens of powers 0.5 D and 20 D respectively, its magnifying power will be

Options

A. 10
B. 20
C. 30
D. 40

Answer

To find the magnifying power of an astronomical telescope, we can use the formula for magnifying power (M):

\[ M = \frac{f_o}{f_e} \]

where:
- \( f_o \) is the focal length of the objective lens,
- \( f_e \) is the focal length of the eyepiece lens.

### Step 1: Understand the relationship between power and focal length
The power (P) of a lens is related to its focal length (f) by the formula:

\[ P = \frac{1}{f} \]

where:
- P is in diopters (D),
- f is in meters (m).

### Step 2: Calculate the focal lengths of the lenses
Given the powers of the lenses:
- Power of the objective lens, \( P_o = 0.5 \, D \)
- Power of the eyepiece lens, \( P_e = 20 \, D \)

Using the formula for power, we can find the focal lengths:

1. For the objective lens:
\[ f_o = \frac{1}{P_o} = \frac{1}{0.5} = 2 \, m \]

2. For the eyepiece lens:
\[ f_e = \frac{1}{P_e} = \frac{1}{20} = 0.05 \, m \]

### Step 3: Calculate the magnifying power
Now we can substitute the focal lengths into the magnifying power formula:

\[ M = \frac{f_o}{f_e} = \frac{2}{0.05} \]

### Step 4: Perform the calculation
Calculating the above expression:

\[ M = \frac{2}{0.05} = 40 \]

### Final Answer
The magnifying power of the astronomical telescope is \( 40 \).

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