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Single slit diffraction takes place when light is incident on a slit with a size comparable to the wavelength of light and an alternating dark and bright pattern can be observed. Diffraction implies the bending of light around the sharp corner of an obstacle. Diffraction can be seen when the sources are small enough that they are fairly the size of light’s wavelength.
| Table of Content |
Key Terms: Diffraction, Single Slit Diffraction, Young’s Single Slit Experiment, Fringe Width, Huygens' Guideline, Wavelength, Light, Wave, Obstacles
What is Diffraction?
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Diffraction is the inclination of a wave produced from a limited source or passing through a limited gap to spread out around obstacles. Diffraction results from the impedance of an endless number of waves transmitted by constant circulation of source focus in a few measurements.
| “Diffraction of light is the bending of light around corners in a way that illuminates the areas that generally are shadowed.” |
For example, the silver lining occurring in the sky is caused by the diffraction of light. Thus, Diffraction is the slight bending of light as it passes around the edge of an object. The measure of the bending of light relies upon the overall size of the frequency of light to the size of the opening. However, if the opening is bigger than the light's frequency, the bend might be unnoticeable.
Relatable Links:
| Concept Related Links | ||
|---|---|---|
| Polarisation | Coherent and Incoherent Addition of Waves | Braggs Law |
| Coherent Sources | Difference Between Diffraction and Interference | Polarization of Light |
What is Single Slit Diffraction?
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Single-slit diffraction can be defined as an observation where the bending of light (or, diffraction) causes the coherent source of light to interfere among themselves in order to produce a certain pattern on the screen, known as the Diffraction Pattern.
When the light goes through a single slit with a width w (frequency of the light), then a single slit diffraction forms on a screen with distance L >> w away from the slit. Huygens' guideline reveals that each piece of the slit can be considered a producer of waves. This load of waves meddles to deliver the diffraction pattern.
Single Slit Diffraction
In other words, if the light is incident on a slit with a width that is comparable to the wavelength of light, then an alternating shadow and bright pattern forms on a screen erected in front of the slit. This phenomenon of light is known as Single Slit Diffraction.
Young's Single Slit Experiment
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According to Thomas Young’s double-slit experiment, performed in 1801, the wave nature of light was demonstrated. In this experiment, monochromatic light was illustrated on two narrow slits. After passing through each slit, the waves superimpose to give an alternate bright and dark distribution on a distant screen. And every bright fringe has the same intensity and width.
Monochromatic light in a single-slit experiment is transferred through one slit of finite width and an identical pattern is observed on the screen. As we move away from the central maximum, unlike the double-slit diffraction pattern, the width and intensity in the single-slit diffraction pattern reduce.
Single Slit Diffraction Formula
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In the event that a monochromatic light of frequency λ falls on a slit of width a, the force on a screen a ways off L from the slit can be communicated as a component of θ. Here, θ is the point made with the first course of light. It is given by,
| I(θ) = Io Sin2α/α2 … (1) |
Here, α = π*λ
Sin θ and I0 are the intensity of the central bright fringe, situated at θ = 0.
Diffraction Maxima and Minima: Bright edges show up at points,
θ = 0, θ = sin-1 (±3λ/2), θ = sin-1 (±5λ/2)
θ = 0 is the focal most extreme.
| Thus, θ= sin-1 ± (2n + 1) λ/2 … (2) |
Dark fringes compared to the condition,
| asinθ = m λ … (3) with m = ± 1, ± 2, ± 3 .. |
In a double-slit arrangement, diffraction through a single slit shows up as an envelope over the obstruction design between the two slits.
Fringe Width
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The angular distance between the two first-order minima (on one or the other side of the centre) is known as the angular width of the central maximum, given by:
| 2θ = 2λa |
The straight width is as per the following,
Δ = L\(\times\)2θ= 2Lλa … (4)
The width of the central maximum in the diffraction formula is in inverse proportion with the slit width. Therefore, if the slit width decreases, the central maximum widens, and if the slit width increases, it narrows down. Hence, it can be concluded from this behaviour that light bends more as the dimension of the aperture becomes smaller.
Central Maximum
The maxima placed between the minima and the width of the central maximum can be expressed as the distance between the 1st order minima from the centre of the screen on either sides of the centre.
Position of minima is expressed by y (which is evaluated from the centre of the screen):
| tanθ ≈ θ ≈ y/D |
Now, for small θ, it can be said:
sin θ ≈ θ
Thus,
⇒ λ = a sin θ ≈ aθ
⇒ θ = y/D = λ/a
⇒ y = λD/a
Width of central maximum is basically twice this value:
⇒ Therefore, Width of central maximum = 2λD/a
⇒ And, Angular width of central maximum = 2θ = 2λ/a
Types of Diffraction
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There are two types of Diffraction:
- Fresnel Diffraction: The light source and the screen both are at limited good ways from the slit. The episode waves are not equal.
- Fraunhofer Diffraction: The light source and the screen both are vastly away from the slit with the end goal that the occurrence of light beams are equal.
Explain the required condition for constructive interference.The constructive interference condition is that the path difference must be equivalent to the integral multiple of the wavelength. Explain Compton effect.Compton effect can be expressed as the effect observed when x-rays or gamma rays are scattered on a material with increase in wavelength. Explain the condition for destructive interference.The destructive interference condition is that the path difference must be equivalent to the odd integral multiple of half wavelength. Define temporal coherence.Temporal coherence can be defined as the correlation between field at one point and the field at the same point later some time. |
Previous Year Questions
- For a crystal, the angle of diffraction … [BITSAT 2008]
- When light is incident on a diffraction grating the zero order … [KCET 2004]
- The width of the diffraction band varies … [KCET 2006]
- A parallel monochromatic beam of light is incident normally on a narrow slit … [JEE Advance 1998]
- Calculate the wavelength of light used in an interference experiment … [BITSAT 2015]
- Two beams of light having intensities … [JEE Advance 2001]
- Angular width of the central maxima in the Fraunhofer diffraction … [NEET 2019]
- For a parallel beam of monochromatic light of wavelength λ … [NEET 2015]
- The angular resolution of a 10 cm diameter telescope at a wavelength of … [NEET 2005]
- The ratio of resolving powers of an optical microscope … [NEET 2017]
- A beam of light of wavelength 600nm from a distant source falls on a single slit … [KCET 2004, UPSEE 2006]
- The aperture diameter of a telescope is 5 m … [JEE Mains 2020]
- The angle of minimum deviation for an incident light ray on an equilateral prism … [KCET 2009]
- In refraction, light waves are bent on passing from one medium … [KCET 2021]
- Two plane wavefronts of light, one incident on a thin convex lens … [KEAM]
Things to Remember
- Diffraction is the inclination of a wave produced from a limited source or going through a limited gap to fan out as it spreads. Diffraction results from the impedance of an endless number of waves transmitted by constant circulation of source focus in a few measurements.
- Fresnel Diffraction: The light source and the screen both are at limited good ways from the slit. The episode waves are not equal.
- Fraunhofer Diffraction: The light source and the screen both are vastly away from the slit with the end goal that the occurrence of light beams are equal.
- For monochromatic light, I(θ) = Io Sin2α/α2
- For Bright Fringes, θ = sin-1 ± (2n+1λ)/2
- For Dark Fringes, asinθ = m λ
Also Read:
Sample Questions
Ques: What do you mean by the Compton effect? (1 mark)
Ans: Compton effect, discovered by Arthur Holly Compton, is the increase in the wavelength of the X-rays and the gamma rays which occurs when they are scattered.
Ques: What is fringe width? (2 marks)
Ans: Fringe width is defined as the distance between two successive bright fringes or two successive dark fringes. In the interference pattern, the fringe width is constant for all the fringes.
Ques: What is meant by phase difference? (2 marks)
Ans: Phase difference is referred to as the difference between any two waves or the particles having the same frequency and starting from the same point. The phase difference is expressed in degrees or radians.
Ques: What is the condition for constructive and destructive interference? (2 marks)
Ans: The condition for constructive interference is that the way contrast ought to be equivalent to an essential variable of the frequency. The condition for destructive interference is that the way contrast ought to be equivalent to an odd fundamental numerous of half frequency.
Ques: Consider a solitary slit diffraction design for a slit width w. It is seen that for the light of frequency 400 nm the point between the primary least and the focal greatest is 4*10-3 radians. What is the worth of w? (3 marks)
Ans: Dark edges in the diffraction example of the single slit are found at points θ for which w*sinθ = mλ, where m is a number, m = 1, 2, 3, ... . For the principal dim periphery we have w*sinθ = λ. Here we are approached to address this condition for w.
Subtleties of the estimation:
First least: w*sinθ = λ, w = (400 nm)/sin(4*10-3 radians) = 1*10-4 m.
Ques: When a monochromatic light source radiates through a 0.2 mm wide slit onto a screen 3.5 m away, the main dim band in the example seems 9.1 mm from the focal point of the brilliant band. What is the frequency of light? (3 marks)
Ans: Dark edges in the diffraction example of a single slit are found at points θ for which w*sinθ = mλ, where m is a whole number, m = 1, 2, 3, ... . For the primary dim periphery we have w*sinθ = λ. Here we are approached to settle this condition for λ.
Subtleties of the estimation:
z = 9.1 mm = 9.1*10-3 m.
L = 3.5 m.
w = 0.2 mm = 2*10-4 m.
L >> z, thus sinθ ~ z/L and λ = zw/(mL).
λ = (9.1*10-3 m)(2*10-4 m)/(3.5 m).
λ = 5.2*10-7 m = 520 nm.
Ques: What is the distinction between the Fresnel and Fraunhofer class of diffraction? (2 marks)
Ans: The light source and the screen both are at limited good ways from the slit for Fresnel diffraction while the distances are endless for Fraunhofer diffraction. The occurrence of light beams is equal (plane wavefront) for the last mentioned. For Fresnel diffraction, the occurrence light can have a circular or barrel-shaped wavefront.
Ques: What is stage contrast? (2 marks)
Ans: The stage distinction is characterized as the contrast between any two waves or the particles having a similar recurrence and beginning from a similar point. It is communicated in degrees or radians.
Ques: What is single-slit diffraction? (2 marks)
Ans: If monochromatic light falls on a thin slit having a width practically identical to the frequency of the episode light, a trademark example of dull and splendid districts is acquired on a screen set before the slit. The waves from each place the slit begin to spread in stage however procure a stage contrast on the screen as they cross various distances. The noticed example is brought about by the connection among force and way contrast.
Ques: What are the conditions for diffraction? (2 marks)
Ans: The conditions for diffraction are as follows:
- The episode light ought to be monochromatic.
- The slit width ought to be practically identical to the frequency of episode light.
Ques: Fraunhofer diffraction at a solitary slit is performed utilizing a 700 nm light. On the off chance that the primary dull periphery shows up at a point of 300, discover the slit width. (3 marks)
Ans: Using the diffraction equation for a solitary slit of width a, the nth dull periphery happens for,
a sin θ= nλ
At point θ=300, the main dull periphery is found. Utilizing n=1 and λ= 700 nm=700 X 10-9m,
a sin 300=1 X 700 X 10-9m
a=14 X 10-7m
a=1400 nm
The slit width is 1400 nm.
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