gen-define-the-resolving-power-of-a-telescope-and-give-one-short-0f39

Define the resolving power of a telescope and give one short worked example.

# Resolving Power of a Telescope ## Definition **Resolving power** is the ability of a telescope to distinguish between two closely spaced objects as separate entities. It is quantified by the **minimum angular separation** (θ) that can be resolved between two point sources. According to the **Rayleigh criterion**, two point sources are just resolved when the central maximum of one diffraction pattern coincides with the first minimum of the other. ## Formula $$\theta = 1.22 \frac{\lambda}{D}$$ where: - θ = minimum resolvable angle (in radians) - λ = wavelength of light - D = diameter of the telescope's objective lens/mirror **Better resolving power** = **smaller θ** (can distinguish closer objects) ## Worked Example **Question:** A telescope has an objective diameter of 200 mm. What is the minimum angular separation it can resolve for visible light (λ = 550 nm)? **Solution:** Given: - D = 200 mm = 0.2 m - λ = 550 nm = 550 × 10⁻⁹ m Using the Rayleigh criterion: $$\theta = 1.22 \frac{\lambda}{D} = 1.22 \times \frac{550 \times 10^{-9}}{0.2}$$ $$\theta = 3.36 \times 10^{-6} \text{ radians}$$ Converting to arc seconds (multiply by 206,265): $$\theta = 0.69 \text{ arc seconds}$$ **Answer:** The telescope can resolve objects separated by at least 0.69 arc seconds.