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.  .