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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