Fringes in Physics, Fringe Pattern and Interference Phenomenon
Waves have an interference phenomenon that gives rise to interference fringes. In the regions where two of the light waves overlap, the waves' electric field vectors add up. Light waves having the same polarization can either constructively or destructively interfere. Waves with constructive interference are in the same phase, and those in destructive waves are 180-degree out of space from one another. Furthermore, waves must maintain their phase relationship and be coherent so that the interference does not change with time.
To ensure that two interfering waves have the same polarization, we split a wave into two with the method called division of wavefront. Then the same wave is passed through two closely spaced slits. This article contains a brief description of what is fringe in physics.
Double Slit
If the light is incident over an obstacle with two smaller slits at a distance d from them, then the wavelets emanating from each of the slits interfere behind that obstacle. Waves passing through each of the slit get diffracted and spread out at the angles where a single slit diffraction pattern results in a nonzero intensity, the waves coming from the slits interferes constructively or destructively. Here is a brief on what is the effect on the interference fringes due to double slit.
[Image will be Uploaded Soon]
If the light falls on a screen kept behind the obstacle, a pattern of dark and bright fringe (stripes) appears on the screen. This pattern of bright and dark lines is called the interference fringe pattern or the interference pattern of light. The brighter lines are the sign of constructive interference, and dark lines indicate destructive interference.
The interference pattern's central fringe is caused by the constructive interference of light from two slits travelling the same distance to the screen and is bright and destructive if it is dark. The central fringe is known as the zero-order fringe. Crest meets the crest, and trough meets the rough.
The darker fringes on the sides of the zero-order fringe are the result of destructive interference. Light from one of the slits travels ½ the wavelength longer than the distance that the light from the other slit travels. At these locations, the crests meet the troughs. The first-order fringes then follow these darker fringes. Light from a slit travels a distance one wavelength longer than the distance that the light from the other slit travels. Then again, the crests meet crests.
The interference fringes' width is most significant at the central fringe of the interference pattern, and then they start decreasing as they move towards the sides.
Formulation of Angles for Interference Fringes
If a light of wavelength λ passes through two slits at a distance d from each other, there will be constructive interference at different angles. We can find these angles by applying the condition for constructive interference, i.e.:
D sinθ = m λ
Here, m = 0, 1, 2, …..
The distance from the slits to the screen differs by the integer number of the wavelengths. Here, crest meets crest.
Now, the angle angles at which the darker fringes can be found (based on the destructive interference condition) are:
D sinθ = (m + ½) λ
Here, m = 0, 1, 2, …..
Now, the distance from the slits to the screen differs by an integer number of wavelength + ½ wavelengths. Here the crest meets the trough.
If we view the interference pattern on a screen at distance L from the slits, the wavelength can be found from the fringes' spacing. We have sinθ = z/(L2 + z2)½ and λ = zd/(m(L2 + z2)½). Here, z is the distance from the interference pattern's centre to the pattern's mth bright light. Now, if L >> z, then (L2 + z2)½ ~ L, and we can write it as:
λ = zd / (mL)
Diffraction Gratings
Diffraction patterns can be created either by a single slit or by double slits. When the light encounters an array of identical and equally-spaced slits, it is known as a diffraction grating. Here, the bright fringe coming from constructive interference from different slits is at the same angles as if they come from two different slits. However, the pattern is just sharper.
FAQs on Interference Fringe
1. What are interference fringes, and how do they form in the double-slit experiment?
Interference fringes are alternating bright and dark bands observed on a screen when coherent light passes through two closely spaced slits. They form because the light waves from each slit overlap, and their electric fields combine either constructively (bright fringe, crest meets crest) or destructively (dark fringe, crest meets trough) depending on their phase difference. This pattern is clear evidence of the wave nature of light as per the CBSE 2025–26 Physics curriculum.
2. How does the distance between slits affect the width and number of interference fringes?
The fringe width (the distance between consecutive bright or dark fringes) is inversely proportional to the distance between the slits (d). As the slit distance increases:
- The fringe width decreases, making fringes narrower.
- The screen can accommodate more fringes within the same span.
This relationship is given by fringe width β = λD/d, where λ is the light's wavelength and D is the distance from the slits to the screen.
3. Why is it necessary to use coherent sources for observing clear interference fringes?
Coherent sources emit waves that have a constant phase difference and the same frequency. They are essential for stable and distinct interference fringes, because:
- Random phase changes cause blurred or washed-out patterns.
- A stable phase relationship ensures that the position of bright and dark fringes does not fluctuate.
This is why light from the same source is usually split into two, ensuring coherence in experiments such as Young’s double-slit.
4. How does replacing monochromatic light with white light affect the observed interference fringe pattern?
When white light (which contains multiple wavelengths) is used instead of monochromatic light, each component wavelength produces its own fringe pattern at slightly different positions. This results in:
- The central fringe remaining white and bright (all wavelengths constructively interfere at the centre).
- Side fringes appearing as colored bands due to overlapping of different wavelengths, creating a spectrum of colors.
5. What is the condition for constructive and destructive interference in a double-slit experiment?
The conditions are derived from the path difference (Δ):
- Constructive interference (bright fringe): Path difference (Δ) = mλ, where m = 0, 1, 2, ...
- Destructive interference (dark fringe): Path difference (Δ) = (m + ½)λ
Here, λ is the wavelength of light and m is the order of the fringe.
6. How can the wavelength of light be determined using interference fringes?
Wavelength (λ) can be calculated by measuring the distance between adjacent bright or dark fringes (β):
λ = (β × d) / D
- β is the fringe width (distance between bright or dark fringes).
- d is the slit separation.
- D is the distance from the slits to the screen.
This method is commonly used in laboratory experiments to measure unknown wavelengths.
7. What is the difference between interference and diffraction patterns?
Interference patterns arise from the superposition of waves from two or more coherent sources (like double slits), resulting in regular, equally spaced fringes. Diffraction patterns occur when light passes through a single slit or obstacle, producing a central bright maximum flanked by progressively fainter and unevenly spaced bands. While interference requires multiple openings, diffraction can occur with a single slit.
8. How does a diffraction grating enhance the sharpness of interference fringes compared to a double-slit arrangement?
A diffraction grating consists of many closely spaced, parallel slits. When light passes through it, numerous diffracted beams reinforce the interference at specific angles, making the bright fringes much sharper and narrower than those produced by a simple double-slit. This high resolution is why diffraction gratings are used for precise wavelength measurement and spectral analysis.
9. What real-world applications depend on the phenomenon of interference fringes?
Interference fringes are utilized in various fields such as:
- Optical testing: Measuring the flatness and surface quality of lenses and mirrors using interferometers.
- Thin film technology: Colors in soap bubbles and oil films result from thin-layer interference.
- Precision wavelength measurements: Devices like Michelson Interferometer use interference for accurate measurements.
- Fiber optics: Interference principles help in data transmission and sensing.
10. What misconceptions do students often have about interference fringes, and how can they be addressed?
Common misconceptions include:
- Believing that light must always produce a visible pattern, ignoring the need for coherent sources.
- Confusing constructive and destructive interference as permanent properties of all waves, not dependent on phase difference and path.
- Assuming both interference and diffraction refer to the same phenomenon.
These misunderstandings can be corrected by visual demonstrations, linking theoretical conditions (like required coherence and phase relationships) to observable patterns, and reinforcing the distinct criteria for interference versus diffraction in the CBSE Physics syllabus.
