EXPERIMENT 7
Object:
- To Determination of the Resolving Power
of a Telescope.
Required
Apparatus:-
Reading
Telescope, Attachment of resolving power of the telescope, Number of patterns
on glass with stand, Incandescent bulb 40w with house on stand, Inch tape.
Theory and Formula
Used:
The
theoretical and practical resolving powers are given by
Theoretical resolving power = λ/a
and practical resolving power = d/D
Where λ = mean wavelength of light employed,
a = width of the rectangular slit for just
resolution of two objects,
d = separation between two object and
D = distance of the objects from the objective of
the telescope.
Hence λ /a = d/D
Rayleigh's
criterion of resolution .According to Rayleigh's criterion, two equally bright
sources can be just resolved by any optical system when their distance apart is
such that in the diffraction pattern, the maximum due to one falls on the
minimum due to the other.
Resolving power of
Telescope.
The resolving power of telescope of a
telescope may be defined as the inverse of the least angle subtended at the
objective by two distant point object which can be just distinguished as
separate in its focal plane.
Let a beam of monochromatic light starting
from a distant object O (not shown) be incident normally on a rectangular
aperture AB fitted in front of the telescope objective .Let AQ represent the
incident wave front which is brought to a focus F and observed magnified by
means of eyepiece. The intensity pattern at F is shown by thick curved
line.
Consider
again an object O' towards to right of O whose pattern is formed towards left
of the F. The pattern is formed at F' as shown by dotted curve. The wave –front
due to the
Incident
light is shown by AN. According to the Rayleigh criterion, the two objects can
only be resolved when the maximum due to one falls on the minimum due to the
other
As the aperture is rectangular the minimum due
to one will fall on the maximum of the other when QN = l. The angle between
the two wave fronts, is,
Where a is aperture and q is the angle
subtended by two objects OO at the objective of telescope.
Again
Where
d is the distance between two objects and D is their distance from the
objective of telescope.
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DIAGRAM:-
Procedure:
1.
Focus the telescope for clear image
far from the telescope.
2.
Keep the incandescent bulb (in lieu
of sodium lamp we have used incandescent bulb to reduce the cost) in the front
of slit pattern
3.
Mount the telescope on a stand such
that its axis lies horizontal and the rectangular lines in first row marked on
pattern board on stand which are vertical. Place the two stands at a suitable
distance (say about 2 meters) fig.
4.
Illuminate the object with source of
light. Now open the slit with the help of micrometer screw and move the
telescope in the horizontal direction such that the images of two vertical
sources are in the field of view of the eyepiece.
5.
Gradually reduce the width of the
slit till the two images just cease to appear as two. Note down the reading of
the micrometer. Again close the slit completely and note down the micrometer
reading. The difference of the two readings gives the width of the slit (a)
just sufficient to resolve the two images.
6.
Width (d) of white or black
rectangular strips in the first row marked on pattern board is one mm.
7.
Measure the distance between the
object and the slit with the help of inch tape which gives D.
8. The
experiment is repeated for different values of D.
Observations: Mean
value of
mm. d=0.5, 1, 2.5 mm
L.C.
of screw = 0.01 mm
S.
No.
|
d
mm
|
Slit
Reading
|
Width
of the
Slit
a = (X – Y)
|
Distance
D
mms.
|
|||||
When
Slit is Closed
|
Slit
when Images Cease
|
||||||||
M.S.
|
VS
|
Total
X
|
M.S.
|
VS
|
Total
Y
|
||||
1.
|
2.5
|
||||||||
2.
|
1.0
|
||||||||
3.
|
0.5
|
||||||||
Calculation:
D = distance
of the objects from the objective of the telescope.
Theoretical
resolving power = λ/a
and practical
resolving power = d/D
Where λ =
mm.
a = width of the rectangular slit for just
resolution of two objects,
d = 2.5, 1.0, 0.5
mms
Hence λ /a = d/D
Result:
The theoretical and practical resolving
powers of the telescope are shown in the table.
Theoretical and
Practical Resolving Powers:
Distance
mm
|
d
mm
|
Theoretical
(l/a) Resolving
Power
|
Practical
(d/D) Resolving Power
|
2.5
|
|||
1.0
|
|||
0.5
|
Precautions and
Sources of Error :
(i)
The axis of telescope should be
horizontal.
(ii) The
rectangular object drawn on the pattern board should be vertical.
(iii)
Backlash error in the micrometer screw
should be avoided.
(iv)
The plane of the slit should be
parallel to the objects.
(v) The
minimum width of slit for resolution should be adjusted very carefully.
The distance D
should be measured from the slit of the telescope to the pattern board.
Viva-Voice
Q.1 What is meant by
Resolving Power?
Ans: It is defined
as the reciprocal of smallest angle subtended at the objective by two distinct
lines (objects) which can be just resolve by the telescope.
Q.2 Why are you
saying just resolve?
Ans: Two point
sources are resolvable only when the central maxima in diffraction pattern of
one falls over the first minimum in the diffraction pattern of the other and
vice-verca.
Q.3 Define Reyleigh
Criterion?
Ans: According to
Reyleigh Criterion, two point sources are resolvable only when the central
maxima in diffraction pattern of one falls over the first minimum in the
diffraction pattern of the other and vice-verca.
Q.4 What do you mean
by diffraction?
Ans: The bending of
light wave around the sharp edge of obstacle and spreading into geometrical
shadow of obstacle in path of light is called diffraction.
Q.5 On what factor
the resolving power of telescope depend?
Ans: Large value of
resolving power, we must have large sized aperture a. Thus, the telescope with
large diameter of the objective has a higher resolving power.
Q.6 Write to
precautions.
Ans: (a) The slit
should be clean as edges and narrow.
(b) Telescope, light source and slit
pattern should be properly arranged
while taking the observation.
Q.7 What is the
relation between resolving power and limit of resolution?
Ans: Resolving Power
= 1 / Limit of resolution
Q.8 What is the
effect on resolving power, when the pattern board taken far from the telescope?
Ans: Resolving power
remain same.
Q.9 Can we increased
a resolving power of telescope, if yes than how?
Ans: Yes, by
increasing the diameter of objective len
Q.10 Which light is
used in the experiment?
Ans: Ordinary light
source is used in the experiment.
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