Download Resolving power

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EXPERIMENT NO. -12
RESOLVING POWER OF A TELESCOPE
Object: To determine the resolving power of a telescope.
Apparatus required: Telescope with the rectangular adjustable slit, a graph paper with
narrow strips on it, travelling microscope and meter scale.
Formula used: The theoretical and the experimental resolving power are given by
Theoretical resolving power=
Practical resolving power=
Where λ=mean wavelength of light employed
a=width of the rectangular slit for the just resolution of two objects.
d=separation between two objects
D=distance of the objects from the objective of the telescope.
Hence
Figure:
O’
O
θ
SLIT
D
A
Q
θ
TWO DISTINCT
LINES
TELESCOP
E
B
N
D
MICROMETER
a
SCREW
F’
F
FIG.-1
FIG.-2
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Theory of the experiment:Rayleigh’s criterion of resolution: According to Rayleigh’s criterion of resolution, 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 of the due
to the other.
Resolving power of telescope: The resolving power of the Telescope may be defined as the
inverse of the least angle subtended at the objective by the two distant point objects which
can be just distinguished as separate in its focal plane.
Let a beam of monochromatic light scattering from a distant object O (not shown) be incident
normally on a rectangular aperture AB fitted in front of the telescope objective. Let AQ
represents the incident wavefront which is brought to a focus F and observed magnified by
means of eyepiece. The intensity pattern at F is shown by thick line.
Consider again an object O` towards the right of O whose pattern is formed towards
the left of 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’s criterion, the two objects can
only be resolved when the maximum due to the one falls on the minimum of the other as
shown in figure 1.
As the aperture is rectangular, the minimum due to the one will fall on the maximum due to
the other when Q=λ.
The angle between the two wave fronts, is,
Θ= =
Where a is the aperture
Θ=is the angle subtended by the two objects OO` at the objective of telescope.
Again
Θ=
Where d is the distance between the two objects and D is their distance from the objective of
the telescope.
Procedure:
i) Mount the telescope on the stand such that its axis lies horizontal and the rectangular
lines marked on cardboard or glass on another stand such that they are vertical.
Place the two stands at a suitable distance (say 3-4 fts.)
ii) Illuminate the object with a 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 the two vertical sources are in the field of view of the eyepiece.
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iii) Gradually reduce the width of the slit till the two images just cease to appearas two.
Note down the reading of the micrometer. Again close the slit completely and note
down the reading of the micrometer. The difference in the two readings will give
the width of the slit ‘a’ just sufficient to resolve the two images.
iv) Measure the width ‘d’ of the black rectangular strips with the help of graph paper/
travelling microscope.
v) Measure the distance ‘D’ between the two objects and the slit.
vi) The experiment is repeated for different values of D.
Observations:
Mean value of
A). Table for width ‘a’ of the slit when micrometer arrangement is attached:Least count of screw of micrometer = ………cm
S.No
Slit readings
Silt when images cease
M.S.
V.S.
Total
Reading Reading X cm
When silt is closed
M.S.
V.S.
Total
Reading
Reading
X cm
Width of Theoreti Distance D
the
slit cal
cm.
a=(X~Y) resolvin
g popup
(
)
1.
2.
3.
4.
5.
B). Measure the distance ‘d’ between the two Objects with the help of graph paper.
Calculation: Should be done on the left side of the practical copy.
Result: A comparison of theoretical and experimental resolving power of the telescope is
shown in the table.
Distance
)
resolving
Theoretical (
) resolving Practical(
power
power
Precautions and Sources of Error:
i) The axis of telescope should be horizontal.
ii) The rectangular object drawn on the paper 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 width ‘a’ should be measured correctly.
vi) The minimum width of slit for resolution should be adjusted very carefully.
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vii) The distance D should be measured from the slit of the telescope to the card-board.