IB Physics Circular Aperture Diffraction

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Tutorial questions on HL Topic 9.4 are given below.

  1. In the equation 𝜽=1.22β‹‹/b, what does 𝜽 represent? ( The Rayleigh resolution criterion states that two point sources of equal intensity can just be resolved with a diffraction-limited optical device with a circular aperture if they are separated in angle by 1.22β‹‹/b radians, where b is the diameter of the aperture collecting light and β‹‹ is the wavelength of the light. The central image of a point source is of angular radius 𝜽 and is called the Airy disc containing 84% of the energy in the image.)
  2. The images of two stars seen through a telescope are just resolved when yellow light is used. Will the images of these stars be seen as distinct when red light is used? (No. Red light increases the diameter of the Airy disc in an image so the Airy discs of each star will overlap more and the images are not resolved. The angle subtended by the stars at the telescope is the same. To obtain greater image resolution the wavelength must be reduced to produce narrower non-overlapping Airy discs in each image.)
  3. Two stars in a binary star system subtend an angle of 2.0 x 10-4 Β° at the Earth. The stars are observed through a telescope in yellow light of wavelength 580 nm. Find the minimum diameter of the telescope that allows the star images to be resolved. (20.0 cm)
  4. Two star images are just resolved when the wavelength of light is β‹‹ and the diameter of the telescope is b. Find the diameter of the telescope that can just resolve the star images in light of wavelength 1.5β‹‹. (1.5b)
  5. Two star images are just resolved when the wavelength of light is β‹‹ and the diameter of the telescope is b. Find the wavelength of the light that can just resolve the images of these stars if a telescope of diameter b/4 is used. (β‹‹/4)
  6. Remember. Angular separation of stars = 𝜽, for resolution 𝜽 ≧ 1.22 β‹‹/b