RESOLVING POWER OF A PLANE DIFFRACTION GRATING THEORY.pptx

This power point explains about resolving power of a plane diffraction grating

1. RESOLVING POWER OF A PLANE DIFFRACTION GRATING

2. The resolving power of a grating is defined as its ability to show two neighboring lines in a spectrum as separate.it is measured by the ratio y/dy . where y is the wavelength of a spectral line and dy is the least difference in the wavelengths of two neighbouring spectral lines which can just be resolved. Light of two wavelengths y and ( y+dy ) is incident normally on the sueface of a plane transmission grating AB.

3. i The light of each wavelengths would form a separate diffraction pattern of the silt P1 is the nth primary maximum of a spectral line of wavelenghth y at an angle of diffraction 0.Then, ( a+b )sin  θ = ny Here ( a+b ) is the grating element. P 2 is the nth primary maximum of a second spectral line of wavelength ( y+dy ) at an angle of diffraction (  θ +d  θ ). Ten, ( a+b )sin (  θ +d  θ )= n( y+dy )

4. According to rayleigh the two spectral lines will appear just resolved if the principal maximum due to ( y+dy ) falls on the first minimum of y or vice versa. Thus the two lines will appear just resolved if the angle of diffraction (  θ +d θ )also corresponds to the direction of first secondary minimum after the nth primary maximum at P 1 corresponds to wavelength y . This is possible if the extra path difference introduced is y/N.

5. Here,N is the total number of lines in the grating ( a+b )sin (  θ +d  θ )= ny+y /N Equating the right hand sides of equ (2) and(3), n( y+dy )= ny =y/N or Ndy =y/N y/ dy = nN

6. The resolving power increases with the order n the spectrum the total number of lines N on the grating .The R.b is independent of the grating element ( a+b ).

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