Single Slit Diffraction

One can observe single slit diffraction when the passing of light takes place via a single slit whose width (w) is on the order of the light’s wavelength. Furthermore, the diffraction pattern on the screen takes place at a distance L >> w away from the slit. Moreover, intensity happens to be a function of angle.

Introduction to Single Slit Diffraction

Experts define diffraction of light as the bending of light around corners such that it spreads out and illuminates areas where one can expect a shadow to form. In general, it is difficult to separate diffraction from interference because the occurrence of both takes place simultaneously. Furthermore, the reason for the silver lining which we witness in the sky is because of the diffraction of light.

In the single-slit diffraction, one can observe the phenomenon of bending of light or diffraction. Moreover, this phenomenon causes light from a coherent source to interfere with itself, thereby resulting in the production of a distinctive pattern on the screen called the diffraction pattern. Furthermore, diffraction is evident when the sources are of very small size, such that they are relatively of the size of the wavelength of light.

Formula of Single Slit Diffraction

Consider that the slit width a << D. x`D is the separation between slit and source. Now, one can identify the angular position of any point on the screen by ϑ whose measurement takes place from the slit centre which divides the slit by a/2 lengths.

In order to describe the pattern, one must first look at the condition for dark fringes. Also, the division of the slit can take place into zones of equal widths a/2. Furthermore, consider a pair of rays whose emanation takes place from distances  a/2 from each other.

The path difference exhibited by the top two rays is:

ΔL= a/2sinΘ

An important point to remember is that this calculation is valid only if D is very large. Furthermore, it is possible to consider any number of ray pairings that start from a distance a/2 from one another. Moreover, one can consider any arbitrary pair of rays at a distance a/2.

For a dark fringe, the path difference must produce destructive interference. Furthermore, the path difference must be out of phase by λ2, with λ being the wavelength.

For the first fringe,

ΔL = λ2 = a/2sinΘ

λ = a sin θ

For a ray emanating from any point in the slit, there exists another ray at a distance a/2 from which destructive interference can take place.

Therefore, at θ = sin − 1λa, there would be destructive interference because any ray emanating from a point has a counterpart that produces destructive interference. As such, one can obtain a dark fringe.

For the next fringe, division of the slit can take place into 4 equal parts of a/4 and the same logic can be applied. Therefore, for the second minima:

λ/2 = a/4sin Θ

2λ = a sin Θ

Similarly, for the nth fringe, division of the slit can take place into 2n parts and this condition can be used as:

nλ = a sin θ

The Central Maximum

The maxima lies between the minima and the width of the central maximum. Furthermore, it simply refers to the distance between the first order minima from the centre of the screen existing on both sides of the centre.

The position of the minima expressed by y (whose measurement takes place from the centre of the screen) is:

tanθ≈θ≈y/D

For small ϑ,

sin θ≈θ

⇒ λ = a sin θ≈aθ

⇒ θ = y/D = λa

⇒ y = λDa

Now, one may ask how to find width of central maximum. Well, the width of the central maximum is simply twice this value

⇒ Width of central maximum = 2λDa

⇒ Angular width of central maximum = 2θ = 2λa

FAQs For Single Slit Diffraction

Question 1: What is meant by diffraction maxima and minima?

Answer 1: The diffraction pattern involves a central bright fringe, also known as the central maxima. Furthermore, central maxima is surrounded by dark and bright lines known as the secondary minima and maxima. Moreover, the central maxima is obtainable at point 0 on the screen.

Question 2: What is meant by single-slit diffraction?

Answer 2: In the single-slit diffraction, observance can be made of the phenomenon of bending of light or diffraction. Moreover, this phenomenon causes light from a coherent source to interfere with itself, which in results in creating a distinctive pattern on the screen called the diffraction pattern.