The distance of moon form the earth is `3.8xx10^(5)` km. Supposing that the eye is most sensitive to the ight of wavelength 550nm, the separation of two points on the moon that can be resolved by a 500cm

Options

A. 50m
B. 55m
C. 51m
D. 60m

Explanation

To solve the problem of determining the separation of two points on the moon that can be resolved by the human eye, we will use the formula for resolving power. Here are the step-by-step calculations:

### Step 1: Understand the Given Data
- Distance of the moon from Earth, \( D = 3.8 \times 10^5 \) km
- Wavelength of light, \( \lambda = 550 \) nm

### Step 2: Convert Units
1. Convert the distance from kilometers to meters:
\[ D = 3.8 \times 10^5 \text{ km} = 3.8 \times 10^5 \times 1000 \text{ m} = 3.8 \times 10^8 \text{ m} \]
2. Convert the wavelength from nanometers to meters:
\[ \lambda = 550 \text{ nm} = 550 \times 10^{-9} \text{ m} \]

### Step 3: Use the Resolving Power Formula
The formula for the minimum resolvable separation \( d \) is given by:
\[ d = \frac{1.22 \cdot D \cdot \lambda}{D} \]
Substituting the values we have:
\[ d = \frac{1.22 \cdot (3.8 \times 10^8) \cdot (550 \times 10^{-9})}{D} \]

### Step 4: Calculate the Resolving Power
Now we can calculate \( d \):
\[ d = \frac{1.22 \cdot (3.8 \times 10^8) \cdot (550 \times 10^{-9})}{1} \]
Calculating the product:
\[ d = 1.22 \cdot 3.8 \cdot 550 \times 10^{-1} = 1.22 \cdot 3.8 \cdot 0.00000055 \]
Calculating this gives:
\[ d \approx 55 \text{ meters} \]

### Conclusion
The separation of two points on the moon that can be resolved by the human eye is approximately **55 meters**.