Question

A plane transmission grating has 800 lines and 0.5 cm width. Light consisting of two doublets I and II falls on it normally. The mean wavelengths of doublets I and II are 6000 and 4200 , respectively, and the wavelength separation for both is 0 6 . Which one of the following is correct in first-order spectrum ?

(a) Both the doublets are not resolved

(b) Doublet I is not resolved, but doublet II is resolved

(c) Both the doublets are resolved

(d) Doublets I is resolved, but doublet II is not resolved

Answer 1

Correct option (b) Doublet I is not resolved, but doublet II is resolved

Explanation:

Resolving power of grating is given as λ/dλ = nN

where n = order of spectrum, N = number of lines in grating

For first order n =1 , λ/dλ = N

Thus, the number of lines required lines on grating is 1000 but actual was 800 , so it cannot be resolved.

Thus, number of required lines on grating is 700 but actual line is 800 . It is resolved.