Class 12 Physics Wave Optics Diffraction in resolving power of telescope

Diffraction in resolving power of telescope

  • In telescope resolving power plays an important role.
  • In telescope there are 2 lenses one is objective lens and other is eye-piece.
  • The purpose of objective lens to create an image at the second focal length of the objective and the first focal length of eyepiece.
  • The image which iscreated will be inverted and diminished.
  • The purpose of eye-piece is just to enlarge the image formed by the objective lens at the focal length.
  • The purpose of objective lens is to resolve images as distinct.
  • For example: -
    • If we are viewing 2 different stars the purpose of objective lens will be to resolve the stars as 2 distinct stars.
  • Whenever a ray of light passes through the objective lens it should get focus at a particular point.
  • But because of the phenomenon of diffraction instead of focussing at a specific point the image gets focussed in and around that area.
  • Limit of Resolution :
    • Limit of resolution is defined as the angle subtended by the distant objects on the objective.
    • This means how small an object can be resolved by the telescope.
    • It is denoted by dθ.
  • Case 1:-The limit of resolution is 0.2 radians.
    • That is telescope can resolve up to 0.2 radians.
  • Case2:- The limit of resolution is 20 radians.
    • The telescope can resolve up to 20 radians.
  • Lesser the limit of resolution better is the resolving power.
    • Resolving Power (R.P) ∝ (1/dθ).
    • dθ∝ (λ/D)
    • =>Limit of resolutiondθ =(1.22 λ/D)
      • Whereλ =wavelength of the wave, D =diameter of the objective lens.
    • If the diameter of the objective lens is large then more and more light can pass through it.
    • As a result telescope will be able to give more detailed image.
    • Resolving Power:
      • Resolving power is defined as the relationship between limit of resolution and resolving power.
      • Resolving Power (R.P) ∝(1/dθ).
      • dθ ∝ (λ/D)
        • Where diameter of the aperture of the convex lens D = (2a) and f=focal length of the lens.
      • When a parallel beam of light is incident on the convex lens it should get focussed at one single point.
      • But diffraction occurs when the distance measured is comparable to the wavelength of the light.
      • Therefore instead of single point a spotappears. This spot appears because of diffraction.
      • There will be one central maximum surrounded by dark band (minima) then secondary maxima and then secondary minima.
      • Experimentally the radius of Central maxima= (1.22λ/D).
      • P of a telescope ∝(D/1.22λ).
    • Conclusion:-A telescope must have a larger diameter objective for better resolution.


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