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प्रश्न
Compare Young’s Double Slit Interference Pattern and Single Slit Diffraction Pattern.
उत्तर
| 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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संबंधित प्रश्न
What is the diffraction of light? How does it differ from interference? What are Fraunhofer and Fresnel diffractions?
Derive the conditions for bright and dark fringes produced due to diffraction by a single slit.
In a biprism experiment, the fringes are observed in the focal plane of the eyepiece at a distance of 1.2 m from the slits. The distance between the central bright and the 20th bright band is 0.4 cm. When a convex lens is placed between the biprism and the eyepiece, 90 cm from the eyepiece, the distance between the two virtual magnified images is found to be 0.9 cm. Determine the wavelength of light used.
Explain experimental setup for Fraunhofer diffraction with neat diagram.
Explain Fraunhofer diffraction at a single slit with a neat ray diagram. Obtain an expression for the width of the central bright fringe.
A lens having focal length f gives Fraunhofer type diffraction pattern of a slit having width a. If wavelength of light is λ, the distance of first dark band and next bright band from axis is given by ____________.
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A parallel beam of monochromatic light of wavelength 5 × 10-7 m is incident normally on a single narrow slit of width 10-3 mm. At what angle of diffraction, the first minima are observed?
In young 's double slit experiment the two coherent sources have different amplitudes. If the ratio of maximum intensity to minimum intensity is 16 : 1, then the ratio of amplitudes of the two source will be _______.
In a Young's double-slit experiment, let β be the fringe width, and let I0 be the intensity at the central bright fringe. At a distance x from the central bright fringe, the intensity will be ______.
The fringe width in a Young's double slit experiment can be increased if we decrease ______.
In Young's double experiment, in air interference pattern second minimum is observed exactly in front of one slit. The distance between the two coherent source is 'd' and the distance between source and screen is 'D'. The wavelength of light source used is ______.
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A mixture of light, consisting of wavelength 590 nm and an unknown wavelength, illuminates Young's double slit and gives rise to two overlapping intererence patterns on the screen. The central maximum of both lights coincides.
Further, it is observed that the third bright fringe of known light coincides with the 4th bright fringe of the unknown light. From this data the wavelength of the unknown light is ______.
In a Young’s experiment, two coherent sources are placed 0.90 mm apart and the fringes are observed one metre away. If it produces the second dark fringe at a distance of 1mm from the central fringe, then the wavelength of monochromatic light used will be ______.
In Young's double slit experiment, the 8th maximum with wavelength λ1 is at a distance d1 from the central maximum and the 6th maximum with a wavelength λ2 is at a distance d2. Then d1/d2 is equal to ______.
In a Young's double slit experiment carried out with light of wavelength λ = 5000 Å, the distance between the slits is 0.2 mm and the screen is at 200 cm from the slits. The central maximum is at x = 0. The third maximum (taking the central maximum as zeroth maximum) will be at x equal to ______.
The angular width of the central maximum of the diffraction pattern in a single slit (of width a) experiment, with λ as the wavelength of light, is ______.
