PHYSICS EXPERIMENT 7

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.

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.