A laser beam of `7,500 Å` is sent from a lunar rover on the moon. If laser beam passes through an aperture of 0.8 cm, calculate the angular spread of diffracted beam on reaching the Earth. The distance between the Earth and the moon is `4 xx 10^5 km`.

Answer

To solve the problem of calculating the angular spread of a diffracted beam from a laser sent from the moon to the Earth, we can follow these steps:

### Step 1: Identify the Given Values
- Wavelength of the laser beam, \( \lambda = 7500 \, \text{Å} = 7500 \times 10^{-10} \, \text{m} = 7.5 \times 10^{-7} \, \text{m} \)
- Aperture diameter, \( b = 0.8 \, \text{cm} = 0.8 \times 10^{-2} \, \text{m} \)
- Distance from the moon to the Earth is not directly needed for calculating the angular spread.

### Step 2: Use the Formula for Angular Spread
The angular spread \( \theta \) for a single slit diffraction can be approximated using the formula:
\[ \theta \approx \frac{\lambda}{b} \]
where \( \lambda \) is the wavelength and \( b \) is the width of the aperture.

### Step 3: Substitute the Values into the Formula
Substituting the values of \( \lambda \) and \( b \):
\[ \theta \approx \frac{7.5 \times 10^{-7}}{0.8 \times 10^{-2}} \]

### Step 4: Calculate \( \theta \)
Calculating the above expression:
\[ \theta \approx \frac{7.5 \times 10^{-7}}{0.8 \times 10^{-2}} = \frac{7.5}{0.8} \times 10^{-5} = 9.375 \times 10^{-5} \, \text{radians} \]

### Step 5: Calculate the Angular Spread
The total angular spread is given by \( 2\theta \):
\[ \text{Angular Spread} = 2\theta = 2 \times 9.375 \times 10^{-5} = 1.875 \times 10^{-4} \, \text{radians} \]

### Final Answer
Thus, the angular spread of the diffracted beam on reaching the Earth is:
\[ \text{Angular Spread} \approx 1.875 \times 10^{-4} \, \text{radians} \]

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