he authors have discussed the variation of resolving power of prism,
grating and reflecting echelon with the value chosen for 1min/1max at limiting resolution,
which is characteristic of the stage of resolution desired and the detecting instrument

Sharma, Om Prakash

Sodha, Mahendra Singh

English

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50  iON DEPENDENCE OF RESO L\|n g  POWER OF PRISM, GRATING AND REFLECTINGlECHELON ON STAGE ’ OF RESOLUTION AND DETECTING INSTRUMENTB y  OM PRAK A SH  SHARM A and M ^HENDRA SINGH SODHA* Department of Physics, AiuhabaI  University, Auahabad(Received fot publication^arch so, igs4)ABSTRACT. The authors have discussed t *  variation of resolving power of pi ism, grating and reflecting echelon with the value cho*n fcr/min/7ma« at limiting resolution, « hich is characterestic of the stage of resolution deiired and the detecting instrument.i n t r o d u c t i o nDilchburn (1930,) has pointed out that the resolving power of an instrument depends upon the stage of resolution desired and the detecting instrument. The stage of resolution and the detecting instrument are characterised by the value of C’=I,mo/I>mx at limiting resolution, where 7min and Imtx are the central minimum and maxima of the resultant intensity pattern of two lines to be resolved.The values of C for three important stages of resolution, distinguished by Ditchburn, when the spectrogram is examined by a roicrophotometer arc as follows :Stage of resolution ... CDetection of inhomogeneity in radiation ... 0.98Partial resolution (approximate measurement ... 0.8of wavelength separation)Complete measurement (measurement of ••• 0.4wavelength separation and relative intensities)This communication discusses the dependence of resolving power of prism, grating and reflecting echelon, which is characterestic the stage of resolution desired and the detecting instrument.V A R I A T I O N  O F  R E S O L V I N G  P O W E R  W I T H  CThe intensity pattern of a spectral line after diffraction by a grating is given by,sin*N)8r = B ' sin*|8 (i)♦ Now at Defence Science Laboratory, New Delhi.438 Om P. Sharma and M. S. Sodhawhere N  is the number of lines In the grating aud ajSsairve (sin t - s in  0) is the phase difference between the rays diffracted by two adjacent elements of grating, where the symbols have usual meanings.The maximum intensity, say Jo, is given by/,=B 2V *and hence equation (i) may be expressed asi l s  _ sin*a:t7~  N*8in*i8~" x 'where x —N P  andEquation (2) also represents the intensity pattern in case of a prism if x = n l v  sin 0, the symbols having usual meanings.The quantity A x  is proportional to the angle between two close spectral lines and therefore we shall use A x  instead of A 6  to represent the latter in this investigation.The intensity distribution of another spectral line separated by an angle A x ^ a  is given bysin (^a: -  a)7o a)* (3)The resulting intensity pattern is given byI  __ sin*a- sin*fjc-a)7o ( x - a YThe central maxima (x"»o)  and minimum [x *^ a ! 2) are given by(4)Lnm sin’ a j (5)and 7»f» _ 2  sin*(a/2) 7„ (a/a)*(6)For limiting resolution... (7)_2sin *(a /2 ) j (  sin*a ... (8)(a/a)* / \I f the separation of two lines at limiting resolution is a it can be shownthat the resolving power R is given byR ^ k t^  for a prism •V. (gafand R^kNn i o f a  grating and for a reflecting echeloq, ...  (qb)where ... ige)Dependence of Resolving Ppwer of Prism, etc. 439Table I  gives the variation of k with C obtained b y. calculating both C and k for some values of a.T abi<b IVariation of Mwith CSerial no. akin degrees in radians :1I 150 5-ir6 ' 1.051 •1.22 160 8—ir9 11t 98 I 1253 165 I .9401 l.r*9i4 170 17i s ’'!.8982 1 0595 175 35,36•8553 1.0286 180 IT .8106 1.007 185i 36.7647 •9738 19018.7199 .9479 195 L3ir12.6747 •9^ 310 2009.6306!.900I I 205 4lir36.5866 .87812 2x0 Z^ir6.5451 .85713 220 43,36•473 •83714 22$ 44640 ■SooIS 230 x8 .3931.770Om P. Sharma and .M. S. SodhaThe variation of k with C is illustrated by the graph belowThe treatment for grating equation (96) is also applicable to reflecting echelon for both have the similar intensity pattern.A C K N O W L E D G M E N T SThe authors are grateful to Prof. K . Banerjee, Dr. K . Majuindar and Shri Keshto Chandra Banerji for their kind interest in the investigation.R E F E R E N C EDitchburn, 1930, Proc. Roy. Irish .4cad., 39,58.

On Dependence of Resolving Power of Prism, Grating and Reflecting Echelon on Stage of Resolution and Detecting Instrument

http://arxiv.iacs.res.in:8080/jspui/bitstream/10821/1850/1/on%20dependence_Om%20Prakash%20Sharam.pdf

On Dependence of Resolving Power of Prism, Grating and Reflecting Echelon on Stage of Resolution and Detecting Instrument

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