The resolving power of a telescope, also known as its angular resolution, is determined by the diameter of its objective lens or primary mirror and the wavelength of the light being observed. To calculate the resolving power, we can use a formula known as the Rayleigh criterion.
The Rayleigh criterion states that the smallest resolvable detail in an image is given by the formula:
θ = 1.22 * (λ / D),
where: θ is the angular resolution (in radians), λ is the wavelength of light (in meters), and D is the diameter of the telescope's objective lens or primary mirror (in meters).
To calculate the resolving power of a 26 cm (0.26 meters) diameter telescope at a wavelength of 550 nm (0.55 μm), we need to convert the wavelength from nanometers to meters:
λ = 0.55 μm = 0.55 × 10^(-6) meters.
Plugging the values into the formula:
θ = 1.22 * (0.55 × 10^(-6) meters / 0.26 meters).
Calculating this expression:
θ ≈ 1.22 * 0.0021154 ≈ 0.002584 radians.
To convert this to arcseconds, we multiply by 206,265 (since 1 radian is approximately equal to 206,265 arcseconds):
θ ≈ 0.002584 * 206,265 ≈ 0.533 arcseconds.
Therefore, the resolving power of a 26 cm diameter telescope at a wavelength of 550 nm is approximately 0.533 arcseconds. This means that the telescope can distinguish between two objects in the sky that are separated by an angle of at least 0.533 arcseconds.