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Relation between Resolving Power and Dispersive Power of a Grating

We know that resolving power

R.P. = λ/d λ nN

and dispersive power  D.p. dθ /D λ =n /(a+b) cos θ n

Therefore,          λ /d λ= nN= N (a+b ) cos θn n /(a+b) cos θn

λ/ d λ =Ax dθ /d λ

Resolving power = total aperture of telescope objective x dispersive power.

The resolving power of a grating can be increased by

(i) Increasing the number of lines on the grating N.

(ii) Increasing the sides of spectrum n.

(iii) Increasing the total width of grating ‘w’, for which one has to make use of whole

aperture of telescopes objective.