Question

Use the formula to calculate the expected angular resolution (α) for each telescope for visible light at a wavelength (λ) of 550 nm (1 nanometer = 1 x 10-9 meters).

a) α = λ/D

b) α = D/λ

c) α = 550 nm * D

d) α = D/550 nm

Answer 1

The correct formula for calculating angular resolution is α = λ/D. For a telescope with a 3.00-mm-diameter pupil and light of 550 nm wavelength, this formula would provide the angle between two just-resolvable points of light.

Step-by-step explanation:

The student is asking about the angular resolution of telescopes, which is a concept in physics dealing with the ability of an optical instrument to distinguish small details of an object. The correct formula to calculate the expected angular resolution (α) for a telescope, when considering visible light at a wavelength (λ) of 550 nm, is α = λ/D.

Using this formula, if we want to find the angular resolution for a telescope with a 3.00-mm-diameter pupil, we would substitute λ with 550 nm (which is 550 × 10-9 meters) and D with 0.003 meters (since 1 mm = 1 × 10-3 meters), and then perform the calculation to obtain the value for α, the angle between two just-resolvable points of light. This involves dividing the wavelength by the diameter of the aperture, which gives us the angular resolution in radians.