Question

Problem 1 - If 1 radian = 206265 arcseconds, what is the resolution formula for arcseconds? Convert 1.22 Radian to arcseconds using ratio. Show your work with units.

Problem 2 - A biologist wants to study deforestation with a satellite camera with a pixel resolution of 10 meters/pixel, which at the orbit of the satellite corresponds to an angular resolution of 6 arcseconds. You have already determined the value for arc seconds from problem number one. To measure the loss of plant matter, she detects the reflection by the ground of chlorophyll, which is the most intense at a wavelength of ___________ (1 nanometer = 10-9 meters) [Use the Electromagnetic Spectrum Below to fill in the blank]. To determine the wavelength, use the electromagnetic spectrum visible light section; what color should chlorophyll reflect? Determine the wavelength using the diagram below. Calculate: What is the diameter of the camera lens that will ensure this resolution at the orbit of the satellite?
There are several steps you need to show for calculating the diameter of the camera lens to receive full credit for problem 2

a. Write the literal equation for the problem. What variable are you solving for? It would help if you manipulated the formula to solve this problem. Show your manipulation in steps.

How to solve literal equations help here.

b. What color should chlorophyll reflect? _____________ Where is the wavelength on the spectrum as far as nanometers? ___________ (this is the wavelength you will use for calculation). Not everyone will have the same wavelength, but it should be similar.

c. Use your literal equation and solve the diameter of the camera lens (You should show all work, and your answer should have one significant figure with units in your response). Circle the answer.
Problem 3 –Since you have already determined the diameter of a lens required for an object with your nanometers from problem #2, you can use this direct relationship to determine the necessary diameter to 10 microns (10 microns = 10,000 nanometers). Choosing the diameter of the lens depends on the wavelength. It would help if you constructed a graph showing the diameter of the lens or the mirror in meters needed to obtain a resolution of 1 arcsecond from far-ultraviolet wavelengths of 200 nanometers to infrared wavelengths of 10 micrometers.

Question: Construct a graph that shows the diameter of a lens or mirror needed to obtain a resolution of 1 arcsecond from far-ultraviolet wavelengths of 100 nanometers to infrared wavelengths of 10 microns (10,000 nanometers). From orbit, a human subtends an angle of 1 arcsecond and emits infrared energy at a wavelength of 10 microns. How large would the camera be to resolve a human by his heat emission?

To solve this problem, you will need to determine

1. Set up graph: Which variable would be on X and Y? Which variable is dependent/independent? Use units!

2. Label the graph with the appropriate scale, including a title.

3. Plot point versus draw a line of best fit starting at zero to determine the answer.
1. What does the spatial resolution of a telescope depend on?



2. The spatial resolution of a telescope is proportional to the wavelength of light being detected divided by the telescope's diameter. Is this a direct or inverse relationship? How does that relate to wavelength versus lens diameter?



3. What is the spatial resolution for our eyes?



4. How is spatial resolution related to remote sensing? (from Module 3 reading assignment)



5. How is the GOES satellite related to this lesson? What exactly does the GOES detect?

Answer 1

Problem 1 - If 1 radian = 206265 arcseconds, what is the resolution formula for arcseconds? Convert 1.22 Radian to arcseconds using ratio. Show your work with units.

Problem 2 - A biologist wants to study deforestation with a satellite camera with a pixel resolution of 10 meters/pixel, which at the orbit of the satellite corresponds to an angular resolution of 6 arcseconds. You have already determined the value for arc seconds from problem number one. To measure the loss of plant matter, she detects the reflection by the ground of chlorophyll, which is the most intense at a wavelength of ___________ (1 nanometer = 10-9 meters) [Use the Electromagnetic Spectrum Below to fill in the blank]. To determine the wavelength, use the electromagnetic spectrum visible light section; what color should chlorophyll reflect? Determine the wavelength using the diagram below. Calculate: What is the diameter of the camera lens that will ensure this resolution at the orbit of the satellite?

There are several steps you need to show for calculating the diameter of the camera lens to receive full credit for problem 2

a. Write the literal equation for the problem. What variable are you solving for? It would help if you manipulated the formula to solve this problem. Show your manipulation in steps.

How to solve literal equations help here.

b. What color should chlorophyll reflect? _____________ Where is the wavelength on the spectrum as far as nanometers? ___________ (this is the wavelength you will use for calculation). Not everyone will have the same wavelength, but it should be similar.

c. Use your literal equation and solve the diameter of the camera lens (You should show all work, and your answer should have one significant figure with units in your response). Circle the answer.

Problem 3 –Since you have already determined the diameter of a lens required for an object with your nanometers from problem #2, you can use this direct relationship to determine the necessary diameter to 10 microns (10 microns = 10,000 nanometers). Choosing the diameter of the lens depends on the wavelength. It would help if you constructed a graph showing the diameter of the lens or the mirror in meters needed to obtain a resolution of 1 arcsecond from far-ultraviolet wavelengths of 200 nanometers to infrared wavelengths of 10 micrometers.

Question: Construct a graph that shows the diameter of a lens or mirror needed to obtain a resolution of 1 arcsecond from far-ultraviolet wavelengths of 100 nanometers to infrared wavelengths of 10 microns (10,000 nanometers). From orbit, a human subtends an angle of 1 arcsecond and emits infrared energy at a wavelength of 10 microns. How large would the camera be to resolve a human by his heat emission?

To solve this problem, you will need to determine

1. Set up graph: Which variable would be on X and Y? Which variable is dependent/independent? Use units!

2. Label the graph with the appropriate scale, including a title.

3. Plot point versus draw a line of best fit starting at zero to determine the answer.

1. What does the spatial resolution of a telescope depend on?

2. The spatial resolution of a telescope is proportional to the wavelength of light being detected divided by the telescope's diameter. Is this a direct or inverse relationship? How does that relate to wavelength versus lens diameter?

3. What is the spatial resolution for our eyes?

4. How is spatial resolution related to remote sensing? (from Module 3 reading assignment)

5. How is the GOES satellite related to this lesson? What exactly does the GOES detect?

Answer 2

Explanation:

Problem 1

The resolution formula for arcseconds is 1 radian = 206265 arcseconds.

To convert 1.22 radians to arcseconds, we can use the conversion ratio of 1 radian = 206265 arcseconds: 1.22 radians x 206265 arcseconds/radian = 252438.3 arcseconds

Problem 2

a. Literal equation: D = (Wavelength / (2* arcsecond))

Variable to solve for: D (diameter of camera lens)

b. Chlorophyll reflects green light. The wavelength of green light on the electromagnetic spectrum is approximately 550 nanometers.

c. D = (Wavelength / (2* arcsecond))

D = (550 x 10^-9 meters / (2* 6 x 10^-6 radians))

D = (550 x 10^-9 meters / 12 x 10^-6 radians)

D = (550 / 12) x 10^-9 meters / 10^-6 radians

D = 45.83 x 10^-3 meters or 0.04583 meters

Problem 3

The graph would have wavelength in nanometers on the x-axis and diameter of lens or mirror in meters on the y-axis.

The graph would start at 100 nanometers and end at 10,000 nanometers on the x-axis and the y-axis would start at 0 and end at the diameter of the lens or mirror needed to obtain a resolution of 1 arcsecond.

The graph would show that as the wavelength increases, the diameter of the lens or mirror needed to obtain a resolution of 1 arcsecond would decrease. At a wavelength of 10,000 nanometers (10 microns), the diameter of the camera would be 0.04583 meters.

The spatial resolution of a telescope depends on the size of the telescope's aperture and the wavelength of light being detected.

The spatial resolution of a telescope has an inverse relationship with the wavelength of light being detected and the telescope's diameter. As the wavelength increases, the spatial resolution decreases, and as the diameter of the telescope increases, the spatial resolution increases.

The spatial resolution for our eyes is about 1 arcminute.

Spatial resolution is related to remote sensing in that it refers to the ability of a sensor to distinguish between two objects that are close together. A higher spatial resolution allows for more detailed information to be gathered from an image.

The GOES (Geostationary Operational Environmental Satellite) detects weather patterns, temperature, humidity, and other atmospheric conditions. It uses remote sensing technology to gather and transmit data to meteorologists for weather forecasting and monitoring.