Question

The fringe width for red colour, as compared to that for violet colour is approximately
(A) three times
(B) double
(C) four times
(D) eight times

Answer 1

Hint
Fringe width is the distance between two successive bright fringes or two successive dark fringes. In the interference pattern, the fringe width is constant for all the fringes. Fringe width is independent of order of fringe. Fringe width is directly proportional to wavelength of the light used.

Complete step by step answer
If the fringe width is 0.75 mm, calculate the wavelength of light. Given: Distance between slits = d = 0.8 mm = 0.8 x $10^{-3}$ m = 8 x $10^{-4}$ m. Distance between slit and screen = D = 1.2 m, Fringe width = X = 0.75 mm = 0.75 x $10^{-3}$ m = 7.5 x $10^{-4}$ m.
For red colour $λ_r$ = 620−750nm and for violet colour $λ_v$ = 380−450nm
So, approximately ${\lambda _r} \cong 2{\lambda _v}$
So, Fringe width $\beta = \dfrac{{\lambda D}}{d}$
Or, ${\beta _r} \cong 2{\beta _v}$
Option (B) is correct.

Note
The distance between any two consecutive bright fringes or two consecutive dark fringes is called fringe spacing. Fringe spacing or thickness of a dark fringe or a bright fringe is equal.