The doublet of the sodium spectrum, in the yellow band, has two constituents hav

Question

The doublet of the sodium spectrum, in the yellow band, has two constituents having lengths of 9 589.0 nm and 589.6 nm, respectively. Light of this doublet is propagated at normal incidence through a crystal slab. The index of refraction of the crystal at these wavelengths is 1.286. The number of waves that are present in a crystal is different for each constituent. The difference in the number of waves, in a particular crystal, is one whole wave. The thickness of the crystal, in mm, is closest to:

Explanation / Answer

The wavelength of light in the crystal==> l' = l/n (n= ref. index of crystal)

number of waves in the crystal of thickness t= t/l'= nt/l

differenting w.r.t. l==> nt (dl/l^2)= 1 (as given in the problem)

==> t= l^2/(n* dl) ; dl = 0.6 nm ; l ~ 589 nm; n= 1.286

substituing the values==> t= (589 *589 *10^(-18)/(1.286*0.6 *10^(-9))) m = 4.5 * 10^(-4) m = 0.45 mm

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