A monochromatic source S1 of wavelength λ1 produces a fringe width β1 in a Young’s double–slit experiment using slit separation d and screen distance D. In a second trial the source is replaced by another source S2 of wavelength λ2; simultaneously the screen is moved so that its distance from the slits becomes D/2 and the slit separation is changed to 3d.
(a) Derive an expression for the new fringe width β2 in terms of λ2, D and d.
(b) Hence obtain the ratio β1β2.
(c) Evaluate β1β2 when λ1=500nm and λ2=400nm.
(d) State clearly whether the fringes in the second trial are wider or narrower than in the first, supporting your answer with the calculated ratio.