In double slit experiment, the angular width of the fringes is `0.20^@` for the sodium light `(lambda=5890Å)`. In order to increase the angular width of the fringes by `10%`, the necessary change in the wavelength is

Options

A. zero
B. increased by 6479 Å
C. decreased by 589 Å
D. increased by 589 Å

Answer

D

Explanation

Let `lambda` be wavelength of monochromatic light incident on slit S, then angular distance between two consecutive fringes, i.e. the angular fringe width is
`theta=(lambda)/(d) " " ` …(i)

where, d is distance between coherent sources.
Given, `(Delta theta)/(theta)=(10)/(100)`
So, from Eq, (i) `(Delta lambda)/(lambda)=(Delta theta)/(theta)=(10)/(100)=0.1`
`rArr Delta lambda=0.1lambda=0.1xx5890 "Å"=589"Å " `(increases)