1.What is the maximum resolution of your eyes (assume the wavelength range that your eyes are sensitive to is 300 – 700 nm and that your iris is ½ cm in diameter.
2.What size eye would be required to see in the radio with the same maximum resolution of your eyes? (use 21 cm for the wavelength of typical radio waves)
3.What is the maximum resolution of the VLBA (longest baseline = 5000 m) at a wavelength of 21 cm?
What is your thinking? We will be happy to critique your work.
did anyone post an asnwer for this?
whats the answer please...
1. To determine the maximum resolution of human eyes, we need to consider the concept of angular resolution. The angular resolution is the smallest angle that two points can be separated by and still be perceived as separate by the eyes.
The formula for calculating angular resolution is given by:
Angular Resolution = 1.22 × (wavelength / diameter)
In this case, we are given that the wavelength range for human eyes is 300 - 700 nm, which we can convert to meters by dividing by 10^9. The diameter of the iris is given as 1/2 cm, which can be converted to meters by dividing by 100.
Let's calculate the maximum resolution of our eyes using the lower end of the wavelength range:
Angular Resolution = 1.22 × (300 nm / (1/2 cm)) = 1.22 × (300 × 10^-9 m / 0.005 m) = 0.079 radians
So, the maximum resolution of our eyes is approximately 0.079 radians.
2. To calculate the size of an eye that can see in the radio wavelength range (wavelength of 21 cm), we can use the same formula for angular resolution:
Angular Resolution = 1.22 × (wavelength / diameter)
Given that the wavelength of typical radio waves is 21 cm, and we want to maintain the same maximum resolution as human eyes, which is 0.079 radians, we can rearrange the formula to solve for the required diameter of the eye:
Diameter = wavelength / (1.22 × Angular Resolution)
Diameter = 21 cm / (1.22 × 0.079 radians) = 276.43 cm
Therefore, an eye with a diameter of approximately 276.43 cm would be required to see in the radio wavelength range with the same maximum resolution as human eyes.
3. The VLBA (Very Long Baseline Array) is a set of radio telescopes that spans across multiple locations. The maximum resolution of the VLBA can be calculated using the formula for angular resolution:
Angular Resolution = (wavelength / baseline)
Given that the wavelength is 21 cm and the longest baseline of the VLBA is 5000 m, we can calculate the maximum resolution:
Angular Resolution = 21 cm / 5000 m = 0.00042 radians
Therefore, the maximum resolution of the VLBA at a wavelength of 21 cm is approximately 0.00042 radians.