The resolution of a telescope is its ability to distinguish specific details in an image. To the right is an example of an image through a low-resolution camera and a high-resolution camera. Which do you think is the high resolution?

Astronomers are always trying to improve the resolution of their telescopes. The resolution of circular apertures, including telescopes, is determined by the equation



where is angular resolution in degrees, is wavelength in meters, and D is diameter of the telescope in meters. The lower is, the better resolution your image will have. For instance, if Telescope A has a resolution of 1 degree, then it can only resolve objects with an accuracy of 1 degree. If Telescope B has a resolution of 1 arcsecond, then it can produce a picture 3,600 times more accurate than Telescope A.

This resolution equation explains why it is so difficult to attain good resolution with a radio telescope. Radio wavelengths are much longer than optical wavelengths, so a much larger radio dish is required to resolve radio images.

Astronomers measure distances in the sky in degrees, arcminutes (denoted with the following symbol: ”), and arcseconds (denoted with the following symbol: ’). Astronomers use a system similar to the system of longitude and latitude that is used to located places on Earth. The system of measurement in the sky is analogous to the system used by geographers, even though astronomers are mapping locations on a much larger globe. Use the following conversions in your calculations:

1 degree = 60 arcminutes (60’)
1 degree = 3600 arcseconds (3600”)
1 arcminute = 60 arcseconds

Do the following calculations using a calculator. Round your answers to 3 significant digits.

1. An optical telescope has a diameter of 1 meter. The astronomer is observing an optical source at a maximum wavelength of 7 × 10^-7 meter. What is the angular resolution of this telescope in arcseconds?
   
   
2. The twin Keck telescopes in Mauna Kea, Hawaii are the largest optical telescopes in the world, each with a diameter of 10 meters. Assuming = 7 × 10^-7 meter, what is the resolution of one of the Keck telescopes in arcseconds?
   
   
3. Using optical interferometry, these telescopes can attain a resolution equivalent to a 90 meter optical dish. Assuming = 7 × 10^-7 meter, what is the resolution of the two Keck telescopes combined in arcseconds?
   
   
4. Consider a 90 meter radio telescope. What resolution can be attained using a wavelength of 21 centimeters (21 × 10^-2 meter)? Compare this resolution to the resolution of one of the 10 m optical Keck telescopes.
   
   
5. The radio dish in Arecibo, Puerto Rico is the largest single-dish radio telescope in the world. The diameter of the dish is 305 meters! Assuming = 21 centimeters (21 × 10^-2 meter), what is the resolution of this radio dish?
   
   
6. Radio interferometry is a very valuable technique, allowing radio astronomers to build high-resolution telescopes without constructing huge dishes. The VLBA has a resolution of 5 × 10^-3 arcseconds when observing radio waves with a wavelength of 21 cm. If you wanted to build a single-dish radio telescope with this resolution, what would the diameter of the dish need to be?
   
   

Solutions