Question

Compare Young’s Double Slit Interference Pattern and Single Slit Diffraction Pattern.

Answer 1

	Young’s double-slit interference pattern:	The single slit diffraction pattern
i.	Dimension of slit: For a common laboratory setup, the slits in Young’s double-slit experiment are much thinner than their separation. They are usually obtained by using a biprism or a Lloyd’s mirror. The separation between the slits is a few mm only.	Dimension of slit: The single slit used to obtain the diffraction pattern is usually of width less than 1 mm.
ii.	Size of the pattern obtained: With the best possible setup, the observer can usually see about 30 to 40 equally spaced bright and dark fringes of nearly the same brightness.	Size of the pattern obtained: Taken on either side, the observer can see around 20 to 30 fringes with the central fringe being the brightest.
iii.	Fringe width W: W = `(λ  "D")/"d"`	Fringe width W: W = `(λ  "D")/"a"` Except for the central bright fringe
iv.	For nth bright fringe
a.	Phase difference, Φ between extreme rays: n(2π)	Phase difference, Φ between extreme rays: `("n" + 1/2)` (2π) OR (2n + 1)π
b.	Angular position, θ: n`(λ/"d")`	Angular position, θ: `("n" + 1/2)(λ/"a")` OR `((2"n" + 1)λ)/(2"a")`
c.	Path difference, ∆l between extreme rays: nλ	Path difference, ∆l between extreme rays: nλ
d.	Distance from the central bright spot, y: n`((λ"D")/"d")` = nW	Distance from the central bright spot, y: `("n" + 1/2)((λ"D")/"a") = ("n" + 1/2)`W
v.	For nth dark fringe
a.	Phase difference, Φ between extreme rays: `("n" - 1/2) (2pi)` OR (2n - 1)π	Phase difference, Φ between extreme rays: n(2π)
b.	Angular position, θ: `("n" - 1/2)(λ/"d")` OR (2n - 1)`λ/(2"d")`	Angular position, θ: n`(λ/"a")`
c.	Path difference, ∆l between extreme rays: `("n" - 1/2)λ` OR `(2"n" - 1)λ/2`	Path difference, ∆l between extreme rays: nλ
d.	Distance from the central bright spot, y': `("n" - 1/2)((λ "D")/"d") = ("n" - 1/2)`W	Distance from the central bright spot, y': n`((λ"D")/"a")` = nW