Resolving Power of Telescopes

• What is the purpose of a circular aperture in a telescope?

  To allow a cone of light to enter
• How does light behave after passing through a circular aperture?

  It acts like a point source
• What happens when two point sources are viewed from a large distance?

  They appear as a single unresolved source
• What occurs when light passes through a circular aperture?

  It diffracts and creates interference fringes
• What is the large central maximum in the diffraction pattern called?

  Airy disc

  
• How wide is the Airy disc compared to the further maxima?

  It is twice as wide
• What is the effect of diffraction on telescope resolution?

  • Diffraction limits detail resolution
  • Larger apertures reduce diffraction
  • Shorter wavelengths improve resolution
• What does the Rayleigh criterion determine?

  Minimum angular resolution of a telescope
• What does the Rayleigh criterion state about two sources?

  They will be resolved if central maximum coincides with first minimum
• How can the resolution of a telescope be increased?

  By increasing the aperture diameter
• What is the equation for angular separation?

  θ = s / d
• What does 's' represent in the angular separation equation?

  Distance between the two sources
• What does 'd' represent in the angular separation equation?

  Distance between the sources and the observer
• What is the formula for the angle of diffraction in single-slit diffraction?

  sin θ = nλ / D
• What does 'n' represent in the diffraction formula?

  Order of the minimum
• What is the significance of the first minimum in determining angular resolution?

  It defines the minimum angular resolution
• What is the small-angle approximation for sin θ?

  sin θ ≈ θ
• What is the expression for minimum angular resolution using the small-angle approximation?

  θ ≈ λ / D
• How is the Rayleigh criterion mathematically expressed for resolvable sources?

  θ > λ / D
• What does the factor of 1.22 represent in the Rayleigh criterion?

  It adjusts for circular apertures
• What is the diameter of the Event Horizon Telescope (EHT)?

  8000 km
• How do you calculate the minimum angular separation for the EHT?

  θ = c / (fD)
• What is the minimum angular separation resolved by the EHT?

  1.63 × 10$^{-10}$ rad
• What is the distance to the supermassive black hole?

  25,000 light years
• How do you calculate the angular size of the black hole?

  θ = s / d
• What is the angular size subtended by the black hole?

  1.01 × 10$^{-10}$ rad
• How does the resolution of the EHT compare to the angular size of the black hole?

  1.63 × 10$^{-10}$ rad > 1.01 × 10$^{-10}$ rad
• What conclusion can be drawn about the EHT's ability to resolve the black hole's detail?

  It cannot suitably resolve the black hole
• What is the implication of the black hole's angular size compared to the EHT's resolution?

  The black hole's size exceeds EHT's resolution
• What should be preferred terminology when discussing telescope resolution?

  Minimum angular resolution
• Why must wavelength and diameter be in the same units?

  To ensure accurate calculations