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

1. RESOLVING POWER OF A PLANE
DIFFRACTION GRATING

3. •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.

4. 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.
•P2 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)

5. •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+dθ)also corresponds to the direction of
first secondary minimum after the nth
primary maximum at P1 corresponds to
wavelength y.
•This is possible if the extra path difference
introduced is y/N.

6. •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

7. 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).

8. THANK YOU