TOPICS TO BE DISCUSSED RESOLVING POWER LORD RAYLEIGH CRITERION RESOLVING POWER OF TELESCOPE RESOLVING POWER OF GRATING RESOLVING POWER The ability of an optical instrument expressed as numerical measure to resolve the images of two nearby points is called resolving power of ins ID: 500313
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Slide1
RESOLVING POWERSlide2
TOPICS TO BE DISCUSSED
RESOLVING POWER
LORD RAYLEIGH CRITERION
RESOLVING POWER OF TELESCOPE
RESOLVING POWER OF GRATINGSlide3
RESOLVING POWER
The ability of an optical instrument, expressed as numerical measure to resolve the images of two nearby points is called resolving power of instrument.Slide4
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 resolvedSlide5
TELESCOPE
Telescope 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/d
ΘSlide6Slide7
BC = AB Sind
Θ
BC
= AB. d
ΘBC =
D.
d
Θ
(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
d
Θ
=
λ
or
d
Θ
=
λ
/D
According to Airy , the condition for circular aperture becomes
d
Θ
=1.22
λ
/D
where
λ
is the wavelength of light used
and
d
Θ
is the limit of resolution of telescopeSlide8
RESOLVING POWER
= 1/limit of resolution
R.P=1/d
θ
=D/1.22λ
if r is the radius of first dark ring or central bright image and f the focal length of the telescope objective then d
θ
=r/f
=1.22
λ
/D
or r=1.22f
λ
/D
The central bright disc is also called as Airy’s disc.
If greater is the diameter then smaller will be the radius.Slide9
RESOLVING POWER OF GRATING
The resolving power of diffraction grating is defined as its ability to show two neighboring lines as separate and is measured by
λ
/d
λSlide10
EXPRESSION FOR RESOLVING POWER:
(a+b)Sin
Θ
n
= ±nλ
condition for minima is
N(a+b)Sin
Θ
n =
±m
λ
……(1)
minima in the direction of (
Θ
n + 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 nSlide11
THANKS