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