Examples of Angular Resolution

The angular resolution equation is

angular resolution (arc sec) = 0.25 wavelength(microns) / diameter(meters)

Example 1 (large telescope)

• diameter of telescope mirror = 1 meter = 100 cm
• wavelength of light = 0.5 micron (visible)
• ang. res. = 0.25 x 0.5 / 1 = 0.125 arc secs

Example 2 (single radio-telescope dish)

• diameter of radio-telescope = 25 meters
• wavelength of radio-wave = 1 meter = 1 x 10 ⁶ microns
• ang. res. = 0.25 x (1 x 10 ⁶) / 25 = 10,000 arc secs
• Much worse than an optical telescope

Example 3 (VLA)

• diameter of radio-telescope = 25 kilometers = 25,000 meters
• wavelength of radio-wave = 1 meter = 1 x 10 ⁶ microns
• ang. res. = 0.25 x (1 x 10 ⁶) / 25,000 = 10 arc secs
• Worse than an optical telescope, but not so bad

Example 4 (inter-continental array of radio-telescopes)

• diameter of radio-telescope = 10,000 kilometers = 1 x 10 ⁷ meter
• wavelength of radio-wave = 1 meter = 1 x 10 ⁶ microns
• ang. res. = 0.25 x (1 x 10 ⁶) / 1 x 10 ⁷ = 0.025 arc secs
• Better than an optical telescope