Relation Between Phase Difference and Path Difference

Relation Between Phase Difference and Path Difference - A Complete Guide

Edited By Vishal kumar | Updated on Jul 02, 2025 05:07 PM IST

Light is the electromagnetic wave and can travel through the vacuum. Vacuum meaning in Hindi is शून्य स्थान. These electromagnetic waves are categorized based on their wavelength or frequency. Wavelength of any electromagnetic wave is given by λ=c/f, where f is the frequency of the wave. Visible light occupies only a small part of the entire electromagnetic spectrum. Electromagnetic waves with shorter wavelengths and higher frequencies include ultraviolet rays, X-rays, and gamma rays. Long-wavelength, low-frequency electromagnetic waves include infrared, microwave, and broadcast television waves. Interference, in physics, the net effect of the combination of two or more wave trains moving on intersecting or coincident paths. Constructive interference happens when two waves are in phase so that their amplitudes are added to form the wave of more amplitude. Constructive meaning in Hindi is रचनात्मक. Constructive meaning in tamil is ஆக்கபூர்வமான(Ākkapūrvamāṉa)

Relation Between Phase Difference and Path Difference - A Complete Guide

The phase difference is the difference in phase angle of the two waves. Path difference is the difference in path of two waves. The meaning of path in Tamil is பாதை (patai). The relationship between phase difference and path deviation is simple. They are proportional to each other. ∅ is called the phase of the wave. The meaning of phase in English is to adjust something to harmonize it with something else. Phase meaning in physics is related to the angle at which waves travel. Phase difference between two waves ranges from 0 to 2π.

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For any two waves with the same frequency, Phase Difference and Path Difference are related as-

Phase difference formula or path difference formula

Δx= 2×∆∅

Where,

Δx is the path difference between the two waves.
Phase difference between two waves is represented by ∆∅

Above equation gives the relation between phase difference and path difference.

What is phase difference?

Phase difference can be defined as the variation of angle between any two waves or the particles having the same rate of frequency and starting from the same point. It is calculated in degrees or radians.

What is the path difference?

Path difference is the difference in path of two waves. Path of the wave can be expressed by its wavelength.

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Phase Difference And Path Difference Equation

The relation between the phase difference and phase angle can be given by the following expressions.

	Formula	Unit
The relation between phase difference and path difference	Δ∅/∆x= 2	No units
Phase Difference	Δ∅= 2×∆x	Radian or degree
Path Difference	Δx= 2×∆∅	meter

Phase Difference Waves

We define the phase difference of a sine wave as the length of time that one wave precedes or follows another. It should be noted that phase difference is not a property of a single wave, it is a property related to two or more waves.

We call the phase difference “Phase Shift” or “Phase Angle”. We represent the phase transition with the Greek letter Phi denoted ?.

The phase difference can be given by the following sine wave:

Figure 1

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Interference:

When two waves of equal wavelength intersect, they combine to form one wave. The resulting wave has the same wavelength as the two interacting waves, but its displacement at any point is equal to the algebraic sum of the displacements of the component waves (superposition principle). The formation of the resulting wave is due to the interference of two individual waves. Interference can be destructive or constructive depending on whether the movements are opposite or in the same direction. Structural interference is demonstrated using monochromatic (single wavelength/color) light, if the light waves combine to form waves of greater amplitude than the individual waves. As for light, the resulting wave will be brighter than the two individual waves. In the case of destructive interference, the amplitude of the resulting wave is smaller than the amplitude of the individual waves and will result in weaker light or no light at all (complete destructive interference).These waves are said to have coherence (the property that two waves of the same wavelength will maintain a constant phase relationship). This is why a laser (an instrument that generates intense, parallel beams of coherent light) is an excellent light source for this lab. When light from both slits hits a point on the screen, constructive or destructive interference occurs. As a result, a light or dark band (edge) will appear on the screen. See figure 2.

Figure 2

When two light waves travel the same distance, they appear on a screen of the same phase and interfere with each other. Waves also interfere with each other (bright fringes) if the difference between the travel distances of each light source is equal to one full wavelength. However, if the difference in the distance the light travels is half a wavelength, then destructive will occur.

Diffraction:

Diffraction: Diffraction refers to the behavior of waves bending around obstacles or passing through small openings. Although light waves have the ability to diffract like other waves, they can be difficult to observe because of their very short wavelength [visible light band: λ (700 nm (red) > > 400 nm (violet)].

$Diffraction$
Figure 3

The curvature of light as it passes through each of the two slits can be explained by Huygens Principle* (any point on the wavefront can be considered a wave source). Since each slit acts as a point light source, the light wave propagates from the slits and deviates from the line. Diffraction patterns are the result of constructive and destructive interference and therefore look like interference patterns. However, in the case of interference, the slits behave like point light sources, while for diffraction the true width of a single slit is taken into account. The amount of light that will bend is determined by the relative size of the light's wavelength relative to the size of the barrier or slit. If the aperture is much larger than the wavelength of light, the curvature will be nearly undetectable. However, if the size difference is small, the amount of light that will be bent will be small.

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NCERT Physics Notes:

Frequently Asked Questions (FAQs)

1. What is the relationship between phase difference and path?

The relationship between phase difference and path deviation is easy to understand. These two are proportional to each other. For any two waves of the same frequency, the phase difference and path difference are related because Δx is the path difference between the two waves, while ΔΦ is the phase difference between two consecutive waves.

2. What is phase difference in geometry?

If the frequencies are different, the phase difference increases linearly at time t. The phenomenon of cyclical change in the cyclic change of reinforcement and resistance is called dams.

3. What is the formula for the difference in paths?

If the distance traveled by the wave from two locations is the same, the path difference is zero. Once you know the path deviation, you can easily find the phase difference using the formula below: Here Δx is the path deviation and the phase difference.

4. What does the phase difference tell us?

We determine the phase difference (ϕ) between two particles or two waves which tells us how far a wave or particle is in front of or behind another wave or particle.

5. What is the relationship between phase difference and path difference in waves?

Phase difference and path difference are directly related in waves. The phase difference is proportional to the path difference. As the path difference increases, the phase difference also increases. Specifically, a path difference of one wavelength corresponds to a phase difference of 360° or 2π radians.

6. Why is understanding the relationship between phase difference and path difference important in interference patterns?

Understanding this relationship is crucial for predicting and explaining interference patterns. Constructive interference occurs when waves are in phase (path difference = nλ), while destructive interference occurs when waves are out of phase (path difference = (2n+1)λ/2). This knowledge helps in determining the locations of bright and dark fringes in interference experiments.

7. How does wavelength affect the relationship between phase difference and path difference?

Wavelength plays a crucial role in the relationship between phase difference and path difference. The phase difference (in radians) is equal to 2π times the path difference divided by the wavelength. This means that for a given path difference, waves with shorter wavelengths will have larger phase differences compared to waves with longer wavelengths.

8. What is meant by "in-phase" waves, and how does it relate to path difference?

"In-phase" waves are waves that have the same phase at a given point in time and space. This occurs when the path difference between the waves is zero or an integer multiple of the wavelength. In other words, waves are in-phase when their path difference is nλ, where n is an integer and λ is the wavelength.

9. How can you determine if two waves are completely out of phase?

Two waves are completely out of phase (also known as antiphase) when their phase difference is 180° or π radians. This occurs when the path difference between the waves is an odd multiple of half a wavelength, i.e., (2n+1)λ/2, where n is an integer and λ is the wavelength.

10. What is the formula relating phase difference (φ) to path difference (Δx) and wavelength (λ)?

The formula relating phase difference (φ) to path difference (Δx) and wavelength (λ) is:

11. How does the medium of wave propagation affect the relationship between phase difference and path difference?

The medium affects this relationship through its impact on the wave's speed and wavelength. In different media, waves may have different speeds and wavelengths for the same frequency. Since the relationship depends on wavelength, changes in the medium can alter the phase difference for a given path difference.

12. Can phase difference be greater than 360° or 2π radians?

Yes, phase difference can be greater than 360° or 2π radians. However, it's often expressed as an equivalent angle within the range of 0° to 360° (or 0 to 2π radians) by subtracting multiples of 360° (or 2π radians). For example, a phase difference of 450° is equivalent to 90°.

13. How does frequency affect the relationship between phase difference and path difference?

Frequency itself doesn't directly affect the relationship, but it indirectly influences it through wavelength. Since frequency (f) and wavelength (λ) are related by the wave speed (v) as v = fλ, a change in frequency results in a change in wavelength for a given medium. This, in turn, affects the phase difference for a given path difference.

14. How does the concept of phase difference and path difference apply to standing waves?

In standing waves, the phase difference between adjacent antinodes is always 180° or π radians. The path difference between these points is always half a wavelength (λ/2). This consistent phase and path difference is what gives standing waves their characteristic node and antinode pattern.

15. Can two waves with different frequencies have a constant phase difference?

No, two waves with different frequencies cannot maintain a constant phase difference over time. Their phase difference will continuously change because they complete their cycles at different rates. This phenomenon is known as beating when the frequency difference is small.

16. What is the relationship between phase velocity and the phase difference-path difference relationship?

Phase velocity is the speed at which a particular phase of the wave (like a crest) travels. It doesn't directly affect the relationship between phase difference and path difference. However, it does determine how quickly a particular phase difference propagates through space.

17. How does the phase difference-path difference relationship apply to Doppler effect?

The Doppler effect doesn't directly involve phase difference and path difference. However, it does affect the perceived wavelength of the wave, which in turn affects the relationship between phase difference and path difference for a given physical separation between two points.

18. How does polarization affect the phase difference-path difference relationship?

Polarization itself doesn't affect the fundamental relationship between phase difference and path difference. However, in some materials (birefringent materials), waves with different polarizations travel at different speeds, which can lead to a phase difference developing between them even if they start in phase.

19. How does the phase difference-path difference relationship apply to quantum mechanical waves?

In quantum mechanics, the wave function of a particle also exhibits phase differences related to path differences. This is crucial in phenomena like the double-slit experiment, where the phase difference between paths leads to an interference pattern in the probability distribution of particle detection.

20. Can phase difference accumulate over long distances? If so, what are the implications?

Yes, phase difference can accumulate over long distances, especially if there's a slight difference in frequency or propagation speed. This can lead to phenomena like wave beating or the need for phase correction in long-distance communications systems.

21. How does the phase difference-path difference relationship apply to quantum entanglement?

While quantum entanglement is a more complex phenomenon, the concept of phase differences is still relevant. In some interpretations, entangled particles can be viewed as waves with a fixed phase relationship, regardless of their separation distance. This leads to the "spooky action at a distance" that Einstein found troubling.

22. How does the phase difference-path difference relationship apply to optical coherence tomography (OCT)?

OCT uses low-coherence interferometry to produce high-resolution images of biological tissues. It relies on measuring the interference between light reflected from the sample and a reference beam. The path difference between these beams results in phase differences, which are used to construct detailed cross-sectional images.

23. How does the concept of phase difference and path difference apply to diffraction patterns?

In diffraction patterns, the path difference between waves from different parts of the aperture or obstacle determines the pattern of constructive and destructive interference. The locations of maxima and minima in the diffraction pattern correspond to specific path differences, which translate to particular phase differences.

24. What is the significance of a path difference of λ/4 (quarter-wavelength)?

A path difference of λ/4 corresponds to a phase difference of 90° or π/2 radians. This is significant because it represents the point halfway between in-phase (constructive interference) and out-of-phase (destructive interference) conditions. It's often used in wave plates and other optical devices to manipulate polarization states.

25. How does the phase difference between two waves change as they propagate through space?

If two waves have the same frequency and are traveling in the same medium, their phase difference remains constant as they propagate. However, if they have different frequencies or are traveling through different media, their phase difference will change over time and distance.

26. How does the concept of phase difference and path difference apply to wave superposition?

In wave superposition, the phase difference between the superposing waves determines whether they interfere constructively or destructively. This phase difference is directly related to the path difference between the waves. The resulting amplitude of the superposed wave depends on both the individual wave amplitudes and their phase difference.

27. Can path difference be negative? If so, what does it mean?

Yes, path difference can be negative. A negative path difference simply means that one wave has traveled a shorter distance than the other. The sign of the path difference affects the sign of the phase difference, but the magnitude of the relationship remains the same.

28. How does the phase difference-path difference relationship apply to reflection of waves?

When a wave is reflected, it undergoes a phase change. For reflection from a denser medium, there's a 180° phase shift, equivalent to a path difference of λ/2. For reflection from a less dense medium, there's no phase shift. This phase change upon reflection is crucial in phenomena like thin-film interference.

29. What is the importance of the phase difference-path difference relationship in noise cancellation technology?

Noise cancellation technology relies on creating sound waves that are 180° out of phase (path difference of λ/2) with the unwanted noise. By understanding the relationship between phase difference and path difference, engineers can design systems that accurately produce these out-of-phase waves to cancel out noise.

30. How does the phase difference-path difference relationship apply to circular motion?

In circular motion, the phase difference between two points on the circle is directly proportional to the angular separation between them. This is analogous to the linear path difference in wave motion. A full circle (360°) corresponds to a phase difference of 2π radians, just as a path difference of one wavelength does in wave motion.

31. What is the significance of a path difference of λ/2 (half-wavelength)?

A path difference of λ/2 corresponds to a phase difference of 180° or π radians. This is significant because it represents the condition for complete destructive interference between two waves of equal amplitude. It's also the phase shift experienced by a wave upon reflection from a denser medium.

32. Can two waves with different amplitudes have the same phase difference?

Yes, two waves with different amplitudes can have the same phase difference. The phase difference is independent of amplitude; it only depends on the relative timing of the waves' cycles. Amplitude affects the intensity of interference but not the phase relationship.

33. What is the role of phase difference and path difference in holography?

In holography, the interference pattern created by the reference beam and the object beam is recorded. This pattern encodes the phase differences resulting from the path differences between these beams. When the hologram is illuminated for viewing, these phase differences are reconstructed, creating a 3D image.

34. What is the significance of a path difference of λ (one full wavelength)?

A path difference of λ corresponds to a phase difference of 360° or 2π radians. This is significant because it represents a full cycle of the wave. Waves with this path difference are in phase and interfere constructively, just like waves with zero path difference.

35. How does the phase difference-path difference relationship apply to seismic waves?

In seismology, the phase difference and path difference between different types of seismic waves (P-waves, S-waves, surface waves) are used to determine the location and characteristics of earthquakes. The relationship helps in interpreting seismograms and understanding the Earth's internal structure.

36. Can phase difference be measured directly? If not, how is it typically determined?

Phase difference cannot be measured directly in most cases. It's typically determined indirectly by measuring the path difference or time delay between waves, or by observing interference patterns. In some electronic applications, phase detectors can measure phase difference directly for electrical signals.

37. How does the phase difference-path difference relationship apply to sound waves in musical instruments?

In musical instruments, the phase difference-path difference relationship is crucial for creating standing waves in strings, air columns, and resonant cavities. The length of a string or air column determines the path differences possible, which in turn determines the frequencies (and thus pitches) that can be produced.

38. What is the importance of the phase difference-path difference relationship in antenna design?

In antenna design, controlling the phase difference between different elements of an antenna array allows for beam steering and shaping. By adjusting the path differences to different elements, the direction of maximum radiation can be controlled, which is crucial for directional antennas and phased arrays.

39. How does the phase difference-path difference relationship apply to X-ray crystallography?

In X-ray crystallography, the path differences between X-rays scattered by different atoms in a crystal lead to phase differences. These phase differences result in an interference pattern that can be analyzed to determine the crystal structure. The relationship between path difference and phase difference is key to interpreting these patterns.

40. What is the role of phase difference and path difference in the formation of rainbows?

Rainbows form due to the interference of light rays that have taken slightly different paths through water droplets. The path differences lead to phase differences, which cause constructive interference at specific angles for different wavelengths of light. This creates the characteristic separation of colors in a rainbow.

41. How does the phase difference-path difference relationship apply to fiber optic communications?

In fiber optic communications, different modes of light can travel with different path lengths through the fiber, leading to phase differences. This can cause modal dispersion, spreading out the signal. Understanding and minimizing these path and phase differences is crucial for high-speed, long-distance optical communication.

42. What is the significance of a path difference of 3λ/4 (three-quarters wavelength)?

A path difference of 3λ/4 corresponds to a phase difference of 270° or 3π/2 radians. This represents a point where two waves are neither fully in phase nor fully out of phase. In some applications, this phase relationship is used to create circular polarization from linear polarization.

43. How does the phase difference-path difference relationship apply to gravitational waves?

Gravitational waves, like other waves, exhibit phase differences related to path differences. In gravitational wave detectors like LIGO, extremely small path differences caused by passing gravitational waves are detected by measuring the resulting phase differences in laser beams.

44. How does the phase difference-path difference relationship apply to electron diffraction?

In electron diffraction, the wave nature of electrons leads to interference patterns similar to those seen with light. The path differences between electrons scattered from different atoms in a material lead to phase differences, resulting in a diffraction pattern that provides information about the material's structure.

45. What is the role of phase difference and path difference in noise reduction headphones?

Active noise reduction headphones use the phase difference-path difference relationship to cancel out unwanted noise. They create sound waves that have a path difference of λ/2 (and thus a phase difference of 180°) compared to the incoming noise, resulting in destructive interference and noise cancellation.

46. How does the phase difference-path difference relationship apply to radar systems?

In radar systems, the phase difference between transmitted and received signals is used to determine the distance to a target (the path difference). More advanced radar systems can use phase differences between signals received by multiple antennas to determine the direction of a target as well.

47. What is the significance of a path difference of 2λ (two full wavelengths)?

A path difference of 2λ corresponds to a phase difference of 720° or 4π radians. This is equivalent to a phase difference of 0° or 2π radians, meaning the waves are again in phase. This illustrates the cyclic nature of phase relationships.

48. How does the phase difference-path difference relationship apply to medical ultrasound imaging?

In ultrasound imaging, the phase differences resulting from different path lengths of reflected sound waves are used to construct images. By precisely measuring these phase differences, the system can determine the depth and location of structures within the body.

49. Can phase difference be used to measure distance? If so, how?

Yes, phase difference can be used to measure distance. By sending a wave and measuring the phase difference between the transmitted and received signals, the path difference (and thus the distance) can be calculated. This principle is used in phase-shift laser rangefinders and some GPS applications.

50. What is the role of phase difference and path difference in the operation of lasers?

In lasers, maintaining a specific phase relationship between the light waves is crucial. The cavity length of the laser determines the path difference for a round trip, which must be an integer multiple of the wavelength for constructive interference. This condition, along with population inversion, allows for the amplification of light in the laser.

51. How does the phase difference-path difference relationship apply to acoustic levitation?

Acoustic levitation uses standing waves to create nodes where objects can be suspended. The phase difference-path difference relationship is crucial in creating these standing waves. By controlling the phase differences between multiple sound sources, stable levitation points can be created and manipulated.

52. Can phase difference be negative? If so, what does it mean?

Yes, phase difference can be negative. A negative phase difference simply means that one wave lags behind the other. For example, a phase difference of -90° is equivalent to a phase difference of 270° or 3π/2 radians. The sign indicates which wave is leading or lagging.

53. What is the importance of the phase difference-path difference relationship in noise reduction in audio systems?

In audio systems, understanding the phase difference-path difference relationship is crucial