Calculate the limit of resolution of a telescope objective having a diameter of `200cm` , if it has detect light of wavelength `500nm` coming from a star.

Options

A. `305xx10^(-9)`radian
B. `610xx10^(-9)`
C. `152.5xx10^(-9)`
D. `457.5xx10^(-9)` radian

Answer

To calculate the limit of resolution of a telescope objective, we will use the formula for the limit of resolution (θ) given by:

\[ \theta = \frac{1.22 \lambda}{D} \]

where:
- \( \theta \) is the limit of resolution in radians,
- \( \lambda \) is the wavelength of light,
- \( D \) is the diameter of the telescope objective.

### Step 1: Identify the given values
- Diameter of the telescope objective, \( D = 200 \, \text{cm} \)
- Wavelength of light, \( \lambda = 500 \, \text{nm} \)

### Step 2: Convert the units
1. Convert the diameter from centimeters to meters:
\[ D = 200 \, \text{cm} = 200 \times 10^{-2} \, \text{m} = 2.00 \, \text{m} \]

2. Convert the wavelength from nanometers to meters:
\[ \lambda = 500 \, \text{nm} = 500 \times 10^{-9} \, \text{m} = 5.00 \times 10^{-7} \, \text{m} \]

### Step 3: Substitute the values into the formula
Now, substitute the values of \( \lambda \) and \( D \) into the formula for the limit of resolution:
\[ \theta = \frac{1.22 \times (5.00 \times 10^{-7})}{2.00} \]

### Step 4: Calculate the limit of resolution
1. Calculate the numerator:
\[ 1.22 \times (5.00 \times 10^{-7}) = 6.10 \times 10^{-7} \]

2. Now divide by the diameter:
\[ \theta = \frac{6.10 \times 10^{-7}}{2.00} = 3.05 \times 10^{-7} \, \text{radians} \]

### Final Result
The limit of resolution of the telescope objective is:
\[ \theta = 3.05 \times 10^{-7} \, \text{radians} \]