Unit 2 Interference of Light | Physical optics -1st sem | Bachelor of Optometry

 

🔹 Interference of Light

Interference of light is a phenomenon where two or more light waves superimpose to form a new wave pattern. This can lead to an increase (constructive interference) or decrease (destructive interference) in light intensity. Interference is one of the strongest proofs of the wave nature of light.

🔶 Definition

Interference is the modification in the distribution of light intensity caused by the superposition of two or more coherent light waves.

🔶 Principle Behind Interference

The phenomenon is based on the Principle of Superposition:

When two or more waves overlap in space, the resultant displacement at any point is the algebraic sum of the displacements due to individual waves.

This creates alternating patterns of bright and dark fringes.

🔶 Conditions for Observing Interference

• Sources must be coherent (same frequency, constant phase difference).
• Waves must have the same wavelength.
• Waves must overlap in space.
• Amplitudes should be nearly equal for visible patterns.
• Waves must be similarly polarized.

🔶 Types of Interference

1. Constructive Interference:

• Path difference: nλ where n = 0, 1, 2,...
• Bright fringe is formed due to increased amplitude.

2. Destructive Interference:

• Path difference: (n + ½)λ
• Dark fringe is formed due to cancellation.

🔶 Real-Life Examples

• Colors in soap bubbles
• Oil films on water
• Young’s Double Slit Experiment
• Newton’s Rings
• Michelson’s Interferometer

🔶 Applications in Optometry

• Measuring wavelengths of light
• Determining refractive indices
• Measuring optical path differences in eye components
• Used in ophthalmic instruments like interferometers

🔶 Mathematical Expression

If two waves of amplitude A₁ and A₂ overlap:

• Resultant intensity: I = (A1 + A2)²
• For equal amplitudes: I = 4A² (maximum)
• For opposite phase: I = 0 (minimum)

🔶 Interference Pattern Diagram

🔶 Summary Table

Type of Interference	Path Difference	Phase Difference	Resulting Intensity
Constructive	nλ	2nπ	Maximum (Bright)
Destructive	(n + ½)λ	(2n + 1)π	Minimum (Dark)

🔶 Conclusion

Interference is a powerful demonstration of the wave nature of light and is widely used in optometry for accurate measurements and diagnostics. Devices like interferometers rely on interference to study fine details of light and eye structures.

🔹 Principle of Superposition

The Principle of Superposition is a core concept in wave theory. It describes how two or more light waves behave when they meet in space. This principle forms the basis of optical interference, diffraction, and even applications in optometry.

🔶 Definition

The Principle of Superposition states that when two or more waves pass through the same point, the resulting displacement is the algebraic sum of the displacements due to each wave individually.

🔶 Mathematical Formulation

Consider two waves:

y₁ = A sin(ωt)
y₂ = A sin(ωt + φ)

Resultant wave:

y = y₁ + y₂ = 2A cos(φ/2) sin(ωt + φ/2)

Resultant Amplitude (A_r):

Ar = 2A cos(φ/2)

Resultant Intensity (I):

I = Ar2 = 4A2 cos²(φ/2)

🔶 Interpretation

• If φ = 0 → waves are in phase → Constructive Interference: I = 4A²
• If φ = π → waves are out of phase → Destructive Interference: I = 0

🔶 Diagram

🔶 Importance in Optics

The principle explains:

• Interference patterns like in Young’s Double Slit Experiment
• Behavior of coherent light sources
• Operation of interferometers
• Fringe analysis in optical systems

🔶 Applications in Optometry

Application	Description
Wavefront analysis	Used in aberrometry for mapping refractive errors
Corneal topography	Interferometric methods for analyzing curvature
Lens quality testing	Detects imperfections in contact and intraocular lenses
Instrument calibration	Used to fine-tune ophthalmic equipment

🔶 Summary Table

Condition	Phase Difference (φ)	Resultant Amplitude (Ar)	Intensity (I)
Constructive	0, 2π, 4π...	2A	4A²
Destructive	π, 3π, 5π...	0	0

🔶 Conclusion

The Principle of Superposition is essential in understanding optical phenomena such as interference and diffraction. In the field of optometry, it provides the theoretical foundation for tools like interferometers and advanced wavefront-guided diagnostics.

🔹 Coherence and Coherent Sources

In optical interference, the concept of coherence is critical. It determines whether two or more light waves can consistently interfere to produce observable patterns. Without coherence, interference effects vanish. This concept plays a foundational role in technologies like interferometry and OCT in optometry.

🔶 What is Coherence?

Coherence refers to a fixed and predictable phase relationship between two or more waves over time.

Coherent waves are "in sync" — maintaining a constant phase difference and often having the same frequency and waveform.

🔶 Types of Coherence

Type	Description
Temporal Coherence	Consistency of phase over time; relates to monochromaticity.
Spatial Coherence	Consistency of phase across different points on a wavefront.

🔶 Temporal Coherence

Temporal coherence is related to the spectral purity of light.

• Coherence time (τ): Time over which phase is predictable.
• Coherence length (L): Distance over which phase remains stable.

L = c × τ   (where c = speed of light)

Lasers have very long coherence lengths. Ordinary bulbs have very short coherence lengths.

🔶 Spatial Coherence

Spatial coherence describes how consistent the phase is across different parts of the wavefront:

• High spatial coherence → flat, uniform wavefront (like lasers).
• Low spatial coherence → irregular wavefront (like LEDs).

🔶 Coherent Sources

Coherent sources emit waves with a constant phase difference, same frequency, and same waveform.

They are essential for producing visible interference patterns. Methods to generate coherent sources include:

• Wavefront division (e.g., Young’s double slit)
• Amplitude division (e.g., Michelson Interferometer)

🔶 Incoherent Sources

• Emit waves with random phase differences.
• Do not produce stable interference patterns.
• Examples: bulbs, candles, sunlight.

🔶 Diagram

🔶 Role in Interference

Property	Coherent Source	Incoherent Source
Phase Relationship	Constant	Random
Interference Pattern	Visible and stable	Not observable
Example	Laser	Filament bulb

🔶 Applications in Optometry

Application	Use of Coherence
Optical Coherence Tomography (OCT)	Uses low-coherence light for high-resolution retinal imaging
Laser Interferometry	High coherence for measuring corneal curvature
Wavefront Aberrometry	Uses coherent light to map refractive errors

🔶 Summary Table

Type of Coherence	Measured By	Related To	Example
Temporal	Coherence Length (L)	Monochromaticity	Laser
Spatial	Coherence Area	Phase consistency over wavefront	LED

🔶 Conclusion

Coherence is essential for producing observable interference. It plays a key role in the design and function of many ophthalmic instruments and diagnostic tools like OCT and interferometers, which are crucial for modern optometric care.

🔹 Constructive and Destructive Interference

When two or more light waves meet, they combine according to the Principle of Superposition. Depending on their phase relationship, this combination can lead to constructive (bright) or destructive (dark) interference. These are the fundamental mechanisms behind all observable interference patterns in optics.

🔶 1. Constructive Interference

Constructive interference occurs when two waves meet in phase, i.e., crest meets crest and trough meets trough, resulting in amplification.

• Condition: Path difference = nλ (n = 0, 1, 2, ...)
• Phase difference: 0, 2π, 4π, ...
• Result: Maximum intensity, bright fringe
• Intensity: I = 4A² (for equal amplitude A)

🔶 2. Destructive Interference

Destructive interference occurs when two waves meet out of phase, i.e., crest meets trough, resulting in cancellation.

• Condition: Path difference = (n + ½)λ
• Phase difference: π, 3π, 5π, ...
• Result: Minimum intensity, dark fringe
• Intensity: I = 0

🔶 Mathematical Expression

For two waves of equal amplitude A:

• Constructive: Ares = 2A, I = 4A²
• Destructive: Ares = 0, I = 0

🔶 Diagram

🔶 Interference Pattern Characteristics

Feature	Constructive	Destructive
Phase Relationship	In-phase	Out-of-phase
Path Difference	nλ	(n + ½)λ
Resulting Intensity	Maximum (Bright fringe)	Minimum (Dark fringe)

🔶 Applications in Optometry

Application	Type	Use
Anti-reflection coatings	Destructive	Reduces glare in lenses
Film layers in IOLs	Both	Improves image contrast
Michelson Interferometer	Both	Precision eye structure measurement
Wavefront aberrometry	Both	Detects high-order refractive errors

🔶 Summary Table

Interference Type	Path Difference	Phase Difference	Resulting Intensity	Example
Constructive	nλ	0, 2π, 4π...	Maximum (Bright)	Film coatings, lasers
Destructive	(n + ½)λ	π, 3π, 5π...	Minimum (Dark)	Anti-reflective lenses

🔶 Conclusion

Constructive and destructive interference explain how light waves interact to form bright and dark patterns. These principles are widely used in optical instruments and vision care technologies to enhance clarity, contrast, and precision in diagnostics and correction.

🔹 Young’s Double Slit Experiment (YDSE)

Young’s Double Slit Experiment, performed by Thomas Young in 1801, is a classic experiment that confirmed the wave nature of light. It demonstrated that light can undergo interference and form patterns of bright and dark fringes due to wave superposition.

🔶 Objective

To demonstrate the interference of light and confirm that light behaves like a wave.

🔶 Experimental Setup

• A monochromatic light source (like a laser or sodium lamp) is directed onto a screen containing two narrow slits S₁ and S₂.
• The slits are placed at a small separation d and act as coherent sources.
• A screen is placed at distance D to observe the interference pattern.
• The overlapping waves create alternating bright and dark fringes due to constructive and destructive interference.

🔶 Diagram

🔶 Conditions for Interference

• Two slits must be coherent sources.
• Path difference must lead to constructive or destructive interference:
• Bright fringe: Δx = nλ
• Dark fringe: Δx = (n + ½)λ

🔶 Fringe Width Derivation

Fringe width (β) is the distance between two adjacent bright or dark fringes.

Let:

• λ = Wavelength of light
• D = Distance between slits and screen
• d = Distance between slits

Formula:

β = (λ × D) / d

🔶 Nature of Interference Pattern

• Central bright fringe occurs at the midpoint where path difference = 0.
• Fringes on both sides are alternating bright and dark and equally spaced.
• Fringe width is constant for monochromatic light.

🔶 Key Terms

Term	Meaning
Central Maxima	Bright fringe at center (Δx = 0)
Fringe Width (β)	Distance between consecutive bright or dark fringes
Order (n)	Indicates nth bright/dark fringe from center

🔶 Factors Affecting Fringe Width

Factor	Effect on Fringe Width
Wavelength (λ)	Increased λ → increased fringe width
Slit Separation (d)	Increased d → decreased fringe width
Screen Distance (D)	Increased D → increased fringe width

🔶 Applications in Optometry

Application	Use in Vision Science
Laser Interferometry	Measure corneal or retinal thickness using fringe patterns
Retinal Imaging	Enhance contrast using optical interference
Wavefront Aberrometry	Fringe distortions used to detect eye aberrations
Lens Quality Testing	Fringe shifts indicate flaws in optical lenses

🔶 Summary Table

Parameter	Value / Formula
Bright Fringe (Maxima)	Δx = nλ
Dark Fringe (Minima)	Δx = (n + ½)λ
Fringe Width (β)	(λ × D) / d
Pattern Nature	Alternating, symmetric, equidistant

🔶 Conclusion

Young’s Double Slit Experiment provided the first direct proof of light’s wave nature. The creation of interference fringes remains fundamental in optics and vision science. Technologies like OCT, aberrometers, and interferometers use similar principles to diagnose and measure fine structures in the eye with great precision.

🔹 Colors of Thin Films

The vibrant and shifting colors seen in soap bubbles, oil spills, and even some insects are a result of thin film interference. This optical phenomenon occurs when light reflects off the top and bottom surfaces of a thin, transparent layer, causing wave interference. It beautifully demonstrates the wave nature of light.

🔶 What is a Thin Film?

A thin film is a layer of material (like oil, soap, or tear film) with a thickness comparable to the wavelength of light. Typical thickness ranges from a few hundred nanometers to a few micrometers. When light reflects off both surfaces of such a film, the reflected rays may interfere with each other, producing constructive or destructive interference depending on path difference and phase shift.

🔶 Mechanism of Thin Film Interference

1. Light hits the upper surface of the film and reflects.
2. Part of the light enters the film, reflects off the bottom surface, and exits the film.
3. The two reflected rays interfere, based on path difference and possible phase change (π shift occurs if reflecting from a denser medium).

🔶 Interference Conditions

Let:

• t = thickness of the film
• n = refractive index of the film
• λ = wavelength of incident light

Optical path difference: Δ = 2nt cos(r)

Constructive interference: (if one phase change)

2nt = (m + ½)λ

Destructive interference: (if one phase change)

2nt = mλ

where m = 0, 1, 2, ...

🔶 Why Do We See Colors?

White light consists of multiple wavelengths. At a particular location on the film, one wavelength may experience constructive interference while others experience destructive interference. This selective enhancement of colors creates the iridescent patterns commonly observed.

🔶 Diagram

🔶 Factors Affecting Thin Film Colors

Factor	Effect
Film Thickness (t)	Changes the optical path difference
Refractive Index (n)	Alters phase change and path length
Wavelength (λ)	Each color has a unique interference condition
Angle of Incidence	Modifies the effective path difference

🔶 Real-Life Examples

• Soap bubbles – variable film thickness creates rainbow-like colors
• Oil on water – multi-layer interference from air/oil/water boundaries
• Insect wings – natural nanostructures cause iridescence

🔶 Applications in Optometry

Application	Description
Anti-reflective Coatings	Thin films reduce glare on spectacle and camera lenses
Tear Film Analysis	Color patterns indicate dry eye or irregular tear layers
Contact Lens Coatings	Thin layers improve comfort and light transmission
Interference Filters	Used in optical instruments to filter specific wavelengths

🔶 Summary Table

Parameter	Role in Interference
Film Thickness (t)	Changes optical path difference → affects color
Refractive Index (n)	Alters both phase change and light speed
Wavelength (λ)	Different wavelengths interfere differently
Applications	AR coatings, diagnostics, contact lens tech

🔶 Conclusion

Thin film interference not only explains beautiful natural phenomena but is also crucial in modern optics. In optometry, it's used in anti-reflective lens coatings, ocular surface diagnostics, and design of high-performance optical devices. Understanding this topic is essential for both practical application and theoretical foundation in vision science.

🔹 Newton’s Rings

Newton’s Rings is a classic interference pattern formed when a plano-convex lens is placed over a flat glass plate. The air film formed between them produces concentric circular fringes due to interference of reflected light. This experiment proves the wave nature of light and is useful in measuring wavelength and lens curvature.

🔶 Experimental Setup

• A plano-convex lens rests on a flat glass plate.
• Monochromatic light is directed vertically from above (e.g., sodium lamp).
• Reflected rays from the top and bottom surfaces of the air film interfere.
• The result is a pattern of bright and dark concentric rings.

🔶 Apparatus

• Plano-convex lens
• Flat glass plate
• Monochromatic light source (e.g., sodium vapor lamp)
• Travelling microscope (for measurements)

🔶 Diagram

🔶 Nature of the Rings

• Rings are circular and concentric.
• The central fringe is dark in reflected light (due to phase reversal).
• Brightness alternates outward in regular fashion.
• Ring spacing decreases with increasing radius.

🔶 Mathematical Derivation

Let:

• R = Radius of curvature of the lens
• λ = Wavelength of light used
• rₙ = Radius of nth dark ring

For dark rings in reflected light:

rₙ² = nλR

rₙ = √(nλR)

n = ring order (1, 2, 3...)

🔶 Key Observations

Feature	Description
Central Spot	Dark (due to π phase change)
Fringe Shape	Concentric circular rings
Fringe Type	Thin film interference (in air)
Fringe Spacing	Decreases outward

🔶 Uses of Newton’s Rings

Application	Purpose
Wavelength Measurement	λ = (rₙ² - rₘ²) / [(n - m)R]
Lens Surface Testing	Detect irregularities via ring distortion
Radius of Curvature	Measure using known wavelength

🔶 Applications in Optometry

Optometry Use	Description
Lens Quality Control	Identifies surface curvature and imperfections
Flatness Testing	Reveals surface deviation via ring shape
Thin Film Uniformity	Checks coatings on IOLs and contact lenses
Wavelength Calibration	Used in setting precision instruments

🔶 Summary Table

Parameter	Formula / Observation
Radius of nth dark ring	rₙ = √(nλR)
Central Fringe	Dark in reflected light
Fringe Type	Concentric rings (non-uniform spacing)
Measurement Uses	λ, R, surface flatness

🔶 Conclusion

Newton’s Rings experiment is a powerful application of thin film interference. Its ability to accurately measure wavelength, determine lens curvature, and detect surface imperfections makes it essential for quality assurance and diagnostics in optometry and ophthalmic industries.

🔹 Determination of Wavelength Using Newton’s Rings

One of the key applications of Newton’s Rings is to accurately determine the wavelength of monochromatic light. By analyzing the diameters of the interference rings formed by a plano-convex lens and a flat glass plate, the wavelength can be calculated with precision. This method is commonly used in optics labs due to its simplicity and accuracy.

🔶 Principle

When monochromatic light reflects from the top and bottom surfaces of the thin air film between a plano-convex lens and a glass plate, interference occurs. The resulting rings can be measured to calculate the wavelength using geometrical and optical relationships.

🔶 Experimental Setup

• Monochromatic light source (e.g., sodium vapor lamp)
• Plano-convex lens placed over flat glass plate
• Interference pattern viewed and measured using a travelling microscope

🔶 Diagram

🔶 Wavelength Formula

From Newton’s Rings theory:

rₙ² = nλR
Dₙ² = 4nλR

To determine wavelength λ using diameters of two rings (n and m):

λ = (Dₙ² - Dₘ²) / [4R(n - m)]

• Dₙ, Dₘ: Diameters of the nth and mth dark rings
• R: Radius of curvature of the lens

🔶 Procedure Summary

1. Set up the Newton’s Rings apparatus with a monochromatic source.
2. Use the microscope to measure diameters of two well-separated rings.
3. Find the radius of curvature (R) of the lens using a spherometer or manufacturer data.
4. Substitute values into the formula to calculate λ.

🔶 Sample Calculation

Given:

• D₁₅ = 3.20 cm
• D₅ = 1.80 cm
• R = 100 cm

λ = (D₁₅² - D₅²) / [4R(n - m)]
   = (10.24 - 3.24) / (4 × 100 × 10)
   = 7 / 4000 = 0.00175 cm = 575 nm

Wavelength = 575 nm

🔶 Important Considerations

• Use higher order rings for better accuracy.
• Ensure lens and plate are clean and aligned properly.
• Radius of curvature R should be known accurately.

🔶 Applications in Optometry and Vision Science

Application	Description
Laser Calibration	Ensures wavelength accuracy in precision instruments
Lens Manufacturing QA	Verifies optical coatings and performance
Wavefront Aberrometry	Requires accurate input wavelength for diagnostics
Spectral Filter Testing	Determines cut-on/off wavelengths in optical filters

🔶 Summary Table

Parameter	Formula / Notes
Radius of nth dark ring	rₙ = √(nλR)
Wavelength (λ)	λ = (Dₙ² - Dₘ²) / [4R(n - m)]
Lens Radius (R)	Measured using spherometer
Best Practice	Use higher-order rings (n ≥ 10)

🔶 Conclusion

Newton’s Rings offers a reliable method for determining the wavelength of light. This is particularly valuable in optometry and optical engineering where precision wavelengths are essential for diagnostics, lens testing, and laser calibration. With a simple experimental setup and careful measurements, this technique delivers high accuracy.

🔹 Air Wedge and Determination of Diameter of a Thin Wire

The Air Wedge experiment uses interference patterns formed in a thin wedge-shaped air film to determine the thickness of a very thin object like a wire or foil. It is based on the principle of interference in thin films and offers a simple method to measure dimensions on the order of micrometers.

🔶 Formation of Air Wedge

• Two optically flat glass plates are placed at a small angle to form a wedge-shaped air film.
• A thin wire is placed at one end to create a uniform slope.
• Monochromatic light is incident normally on the setup.
• Light reflects from both the top and bottom surfaces of the air wedge, causing interference.

🔶 Diagram

🔶 Nature of Fringes

• Fringes are straight, parallel, and equally spaced.
• They appear due to constructive and destructive interference.
• The central fringe is dark due to a phase shift of π (180°) upon reflection.

🔶 Fringe Width and Thickness Formula

Let:

• λ = Wavelength of light
• L = Length of the air wedge
• t = Thickness of the wire (to be calculated)
• β = Fringe width (distance between two dark fringes)

Fringe width:

β = λL / (2t)

To find thickness:

t = λL / (2β)

🔶 Experimental Procedure

1. Place a thin wire between two glass plates to form an air wedge.
2. Illuminate with a monochromatic light source (e.g., sodium lamp).
3. View the interference pattern with a travelling microscope.
4. Measure the distance between consecutive dark fringes (β).
5. Measure wedge length (L) using a scale or microscope.
6. Use the formula to calculate wire thickness t.

🔶 Sample Calculation

Given:

• λ = 600 nm = 6 × 10⁻⁵ cm
• L = 4 cm
• β = 0.05 cm

t = (λ × L) / (2 × β)
  = (6 × 10⁻⁵ × 4) / (2 × 0.05)
  = 2.4 × 10⁻³ cm = 24 μm

Wire diameter = 24 μm

🔶 Applications in Optometry

Application	Description
Thin Film Measurement	Determine coatings or surface layers on lenses
Lens Coating Quality	Fringe patterns reveal coating uniformity
Component Flatness Testing	Straight fringes confirm flatness of glass or lens surfaces
Wire/Foil Thickness Testing	Used in precise optical instruments and surgical tools

🔶 Summary Table

Parameter	Formula / Notes
Fringe Width (β)	β = λL / (2t)
Thickness (t)	t = λL / (2β)
Fringe Nature	Straight, equally spaced, dark and bright
Central Fringe	Dark (due to phase reversal)

🔶 Conclusion

The Air Wedge method is a highly effective and precise technique for measuring the thickness of thin wires and films. In the field of optometry, it helps ensure the accuracy and quality of lenses, coatings, and other fine components in optical devices.

🔹 Michelson’s Interferometer – Construction, Working, and Applications

The Michelson Interferometer is a highly precise optical instrument used to measure wavelengths, refractive indices, and small distances. Invented by Albert A. Michelson, it works on the principle of interference of light. This device is also a foundational concept behind advanced ophthalmic imaging systems like Optical Coherence Tomography (OCT).

🔶 Construction

The main components include:

• Monochromatic Light Source – e.g., laser or sodium lamp
• Beam Splitter (G) – a partially silvered glass plate that splits the light beam
• Two Mirrors:
  • M1 – movable mirror
  • M2 – fixed mirror
• Compensating Plate (C) – ensures equal glass path in both arms
• Screen or Telescope (T) – to observe interference fringes

🔶 Diagram

🔶 Working Principle

• Light beam is split by the beam splitter into two perpendicular arms.
• Each beam reflects off a mirror (M1 and M2) and returns to the splitter.
• The returning beams interfere, producing a pattern of bright and dark fringes.
• Fringes shift when the movable mirror (M1) is displaced.

🔶 Types of Fringes

Fringe Type	Condition
Circular Fringes	Perfect mirror alignment
Straight Fringes	Slight mirror tilt

🔶 Wavelength Measurement

If mirror M1 is moved by a distance d and N fringes are counted:

λ = 2d / N

🔶 Applications

Application	Description
Wavelength Determination	Accurate measurement using fringe count
Refractive Index Measurement	Fringe shift when air is replaced with a gas
Lens Surface Testing	Detects irregularities on optical surfaces
Thin Film Thickness	Calculates optical thickness via fringe movement
Calibration of Instruments	High precision optical setups use Michelson designs

🔶 Use in Optometry

Optometry Application	Usage
OCT Imaging	Based on Michelson interferometry to image retina and cornea
Laser Aberrometry	Detects minute visual defects using interference
Contact Lens Testing	Examines thickness and uniformity of lens material
Slit Lamp Calibration	Uses fringe shifts for system alignment

🔶 Fringe Shift Formula

When N fringes shift due to mirror movement d:

N = 2d / λ

🔶 Advantages

• High accuracy for small measurements
• Capable of detecting sub-micron distances
• Used for both monochromatic and white light
• Applicable in scientific, industrial, and clinical fields

🔶 Limitations

• Requires precise alignment
• Highly sensitive to vibrations and temperature
• Fringe interpretation needs expertise

🔶 Summary Table

Parameter	Formula / Notes
Wavelength (λ)	λ = 2d / N
Interference Conditions	Δx = nλ (bright), Δx = (n + ½)λ (dark)
Fringe Nature	Circular or straight
Main Uses	Wavelength, refractive index, flatness, imaging

🔶 Conclusion

The Michelson Interferometer is a foundational instrument in both classical optics and modern ophthalmic imaging. It enables the measurement of extremely small distances and changes in optical path length. Its principles are actively applied in optometry devices like OCT, aberrometers, and precision laser systems.

For more units of physical optics click here 👇

👉 Unit 1 Nature of light (Part 1)

👉 Unit 1 Interference of Light (Part 2)

👉 Unit 3 Diffraction and Scattering 

👉 Unit 4 Polarization of Light 

👉 Unit 5 LASERS