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RESOLVING POWER

RESOLVING POWER. TOPICS TO BE DISCUSSED. RESOLVING POWER LORD RAYLEIGH CRITERION RESOLVING POWER OF TELESCOPE RESOLVING POWER OF GRATING.

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RESOLVING POWER

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  1. RESOLVING POWER

  2. TOPICS TO BE DISCUSSED • RESOLVING POWER • LORD RAYLEIGH CRITERION • RESOLVING POWER OF TELESCOPE • RESOLVING POWER OF GRATING

  3. RESOLVING POWERThe ability of an optical instrument, expressed as numerical measure to resolve the images of two nearby points is called resolving power of instrument.

  4. Lord Rayleigh criterion According to this, the two nearby images are said to be just resolved if the position of central maxima of diffraction pattern of one coincides with first secondary minima of diffraction pattern other and vice versa. (a) Easily resolved(b) Just resolved(c) not resolved

  5. TELESCOPETelescope is used to see distant objects and therefore the amount of details given by it depends on the angle subtended at its objective by the two point objects.RESOLVING POWER OF A TELESCOPE The resolving power of a telescope is defined as the reciprocal of smallest angle subtended at the objective by the two distant objects which can be seen just as separate in the telescope. R.P=1/dΘ

  6. BC = AB SindΘBC= AB. dΘBC = D.dΘ (for small angles)If path difference is λ , then the position P’ corresponds to first minima of the first image. But P’ is the position of central maxima of second image . Hence according to Rayleigh criteria of just resolution D dΘ=λor dΘ= λ/D According to Airy , the condition for circular aperture becomes dΘ=1.22 λ/Dwhere λ is the wavelength of light used and dΘ is the limit of resolution of telescope

  7. RESOLVING POWER= 1/limit of resolution R.P=1/dθ =D/1.22λif r is the radius of first dark ring or central bright image and f the focal length of the telescope objective then dθ=r/f =1.22λ/Dor r=1.22fλ/DThe central bright disc is also called as Airy’s disc.If greater is the diameter then smaller will be the radius.

  8. RESOLVING POWER OF GRATINGThe resolving power of diffraction grating is defined as its ability to show two neighboring lines as separate and is measured by λ/dλ

  9. EXPRESSION FOR RESOLVING POWER:(a+b)SinΘn = ±nλcondition for minima isN(a+b)Sin Θn = ±mλ……(1)minima in the direction of (Θn +dΘn ) is given as N(a+b)sin(Θn +dΘn ) =(nN+1)λ……..(2)according to Rayleigh criterion if the wavelength λ and λ+dλ are to be resolved by grating , the nth principal maxima of λ+dλ must be in the direction of Θn +dΘn and is given as (a+b) sin(Θn +dΘn ) = n(λ+dλ )…………(3)N (a+b) sin(Θn +dΘn ) = N n(λ+dλ )…………(4)On comparing (2) and (4)(nN+1)λ = Nn(λ+dλ) λ /dλ=N n

  10. THANKS

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