Single Slit Diffraction Formula
Denote the slit width as ‘a’, and the distance between the slit and the screen as D such that a<<<D.
The angular location of any point on the screen will be determined by measuring from the slit centre, which splits the slit by a ⁄ 2 lengths. To explain the pattern, we’ll look at the state of black fringes first. Let us also split the slit into equal-width zones a ⁄ 2. Let’s take a look at a pair of rays that come from a ⁄ 2 distances apart, as illustrated below.
The top two rays indicate the following route difference:
Δ L = (a ⁄ 2) sinθ
Note: Remember that this is only a viable computation if D is really large.
Any number of ray pairs that start at a distance of a ⁄ 2 from one another, such as the bottom two rays in the diagram, can be considered. Any arbitrary pair of rays separated by a ⁄ 2 can be taken into account. In a minute, we’ll discover how important this method is.
The path difference must create destructive interference for a dark fringe; the path difference must be out of phase by λ ⁄ 2. (λ represents the wavelength)
For the first fringe,
Δ L = λ ⁄ 2 = a ⁄ 2 sinθ
λ = a sinθ
There is another beam at a distance of a ⁄ 2 that can create destructive interference for a ray coming from any point in the slit. As each ray originating from a point has a counterpart that produces destructive interference, there is destructive interference at θ = sin−1(λ ⁄ a). As a result, a dark fringe is created.
We may divide the slit into four equal portions of a ⁄ 4 and use the same rationale for the next fringe. As a result, for the second minima,
λ ⁄ 2 = a ⁄ 4 sinθ
2λ = a sinθ
Similarly, we may divide the slit into 2n parts for the nth fringe and utilise the following condition:
λ ⁄ 2 = a ⁄ 2n sinθ
n λ = a sinθ
Diffraction of light
Diffraction is a phenomenon shown by light. When the wave of light interacts with the particle in the atmosphere it bends at the corners and scatters in the area to illuminate the whole area, this phenomenon is called the Diffraction of light. It is a property of light which is used to explain various phenomena observed in our daily life.
Let’s learn about diffraction in detail in this article.
Table of Content
- What is Diffraction?
- Diffraction Examples
- Types of Diffraction
- Single Slit Diffraction
- Single Slit Diffraction Formula
- Central Maximum
- Resolving Power
- Rayleigh’s Criterion
- What Is the Difference Between Diffraction and Scattering?
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