Unit-4. LASER and Fiber Optics - Solutions

Part A: Short Answers (1 or 2 marks)

(1) Write Snell's law

Answer: Snell's law states that when light passes from one medium to another, the ratio of sine of angle of incidence to the sine of angle of refraction is constant and equal to the ratio of refractive indices of the two media.

Mathematical form:

n₁ sin θ₁ = n₂ sin θ₂

or

sin i / sin r = n₂ / n₁ = constant

Where:

n₁ = refractive index of first medium
n₂ = refractive index of second medium
θ₁ (or i) = angle of incidence
θ₂ (or r) = angle of refraction

(2) Write full form of LASER

Answer: LASER stands for Light Amplification by Stimulated Emission of Radiation.

L - Light
A - Amplification
S - Stimulated
E - Emission
R - Radiation

(3) What is monochromatic light and polychromatic light?

Answer:

Monochromatic Light: Light consisting of only one wavelength or single color. It has a single frequency and energy. Example: Laser light, sodium vapor lamp light.

Polychromatic Light: Light consisting of multiple wavelengths or many colors. It contains waves of different frequencies. Example: White light, sunlight.

(4) Write properties of laser light

Answer: Properties of laser light are:

Monochromaticity - Single wavelength/color (single frequency light)
Coherence - All waves are in phase (temporal and spatial coherence)
Directionality - Highly directional beam, propagates in one specific direction with minimal divergence
High Intensity - Concentrated energy in a narrow beam, very powerful and bright
Polarization - Waves vibrate in a single plane
Low Divergence - Beam remains parallel even after traveling long distances
Focused Beam - Can be focused to a very small area, depositing energy in a tiny spot
High Speed - Travels at tremendous velocity (speed of light)

(5) Define: Absolute refractive index, Critical angle

Answer:

Absolute Refractive Index: The ratio of speed of light in vacuum (or air) to the speed of light in that medium.

n = c / v

Where:

n = absolute refractive index
c = speed of light in vacuum (3 × 10⁸ m/s)
v = speed of light in the medium

Critical Angle: The angle of incidence in the denser medium for which the angle of refraction in the rarer medium becomes 90°. Beyond this angle, total internal reflection occurs.

sin θc = n₂ / n₁  (where n₁ > n₂)

Part B: Detailed Answers (2 or 3 marks)

(1) Explain refraction of light with figure and examples

Answer:

Refraction of Light: The phenomenon of change in direction (bending) of light when it passes from one transparent medium to another is called refraction. This occurs because the speed of light varies in different media.

Diagram:

$Refraction through Glass Slab$

ASCII Representation:

    Air (Rarer Medium - n₁)
         |
      PQ |  ← Normal N₁
    i ↗  |  
   P/___Q|______________ AB (Glass Surface)
     ↘  |
   r  ↘ |  Glass (Denser Medium)
       ↘|  
        R  ← Refracted Ray QR
        |
        |  ← Normal N₂
     e ↗|  
      / |______________ CD (Glass Surface)
     /  |
    S   |  Air (Rarer Medium)
        ↓  Emergent Ray RS

Explanation:

When light travels from rarer to denser medium (air to glass), it bends towards the normal (θ₂ < θ₁)
When light travels from denser to rarer medium (glass to air), it bends away from the normal (θ₂ > θ₁)
The bending occurs because light travels at different speeds in different media

Examples:

A pencil partially immersed in water appears bent
A coin at the bottom of a water-filled vessel appears raised
Twinkling of stars due to atmospheric refraction
Formation of mirages in deserts
Lenses in spectacles correct vision through refraction

(2) Explain refractive index. What is absolute refractive index?

Answer:

Refractive Index: It is a measure of how much light slows down when it passes through a medium. It determines the bending of light rays at the interface between two media.

Types:

Relative Refractive Index: The ratio of speed of light in first medium to speed of light in second medium.
```
n₂₁ = v₁ / v₂ = n₂ / n₁
```
Absolute Refractive Index: The ratio of speed of light in vacuum (or air) to the speed of light in that medium.
```
n = c / v
```
Where:
- c = 3 × 10⁸ m/s (speed of light in vacuum)
- v = speed of light in the medium

Properties:

Always greater than 1 for any medium (except vacuum where n = 1)
Higher refractive index means light travels slower in that medium
Depends on wavelength of light (causes dispersion)

Refractive Indices of Common Materials (at 20°C):

Medium	Refractive Index
Vacuum/Air	1.000
Ice (0°C)	1.31
Water	1.333
Ethyl Alcohol	1.362
Glycerine	1.473
Glass/Benzene	1.501
Quartz	1.554
Polystyrene	1.595
Diamond	2.417

Key Points:

Optically denser medium has higher refractive index
Optically rarer medium has lower refractive index
Higher n means light travels slower in that medium

(3) Explain total internal reflection in detail with figure

Answer:

Total Internal Reflection (TIR): When light traveling from a denser medium to a rarer medium is completely reflected back into the denser medium at the interface, the phenomenon is called total internal reflection.

Conditions for TIR:

Light must travel from denser to rarer medium (n₁ > n₂)
Angle of incidence must be greater than critical angle (i > θc)

Diagram from Textbook:

Total Internal Reflection

Figure: Total internal reflection in water showing light rays at different angles - some refracted, one at critical angle, and some totally reflected

Critical Angle Illustration

Figure: Derivation of critical angle formula using Snell's law

ASCII Representation:

        Denser Medium (Water - n₁)  |    Rarer Medium (Air - n₂)
                                    |
    A        B         C            |
     \       |        /             |
      \      |       /              |
    θ₁ \     |θc    / θ₃            |
        \    |     /                |
         \   |    /                 |    
          \  |   /                  |
___________\◄|__/___________________| 90° (Critical Ray)
            \|_/                    |
             X                      |
            /|\                     |
           / | \                    |
          /  |  \                   |
         /   |   \                  |
       r₁   TIR  r₃                 |
     (Reflected)  (Totally Reflected)|
                                    |

Explanation:

Ray A: i < θc → Refraction occurs (bends away from normal)
Ray B: i = θc → Refracted ray grazes along the surface (r = 90°)
Ray C: i > θc → Total internal reflection occurs

Critical Angle Formula:

sin θc = n₂ / n₁  (where n₁ > n₂)

or

θc = sin⁻¹(n₂ / n₁)

Examples of Critical Angles:

Glass-Air Interface:
- n₁ (glass) = 1.50, n₂ (air) = 1.00
- θc = sin⁻¹(1.00/1.50) = sin⁻¹(0.667) = 41.1°
Water-Air Interface:
- n₁ (water) = 1.33, n₂ (air) = 1.00
- θc = sin⁻¹(1.00/1.33) = sin⁻¹(0.752) = 48.75°
Diamond-Air Interface:
- n₁ (diamond) = 2.42, n₂ (air) = 1.00
- θc = sin⁻¹(1.00/2.42) = sin⁻¹(0.413) = 24.4°
- This small critical angle explains diamond's brilliant sparkle

Applications:

Optical fibers for data transmission
Prisms in periscopes and binoculars
Brilliance of diamonds (due to very small critical angle)
Mirage formation in deserts
Endoscopy in medical field
Sparkling of crystal glass

(4) Give difference between common light and laser light

Answer:

Property	Common Light	Laser Light
Monochromaticity	Polychromatic (multiple wavelengths)	Monochromatic (single wavelength)
Coherence	Non-coherent (waves out of phase)	Highly coherent (waves in phase)
Directionality	Spreads in all directions	Highly directional, narrow beam
Divergence	High divergence	Very low divergence (parallel beam)
Intensity	Low intensity	Very high intensity
Source	Spontaneous emission	Stimulated emission
Polarization	Unpolarized or randomly polarized	Polarized
Energy	Low energy density	High energy density
Phase relationship	Random phase	Constant phase relationship
Example	Bulb, tube light, sunlight	He-Ne laser, CO₂ laser, ruby laser

Visual Comparison from Textbook:

Light Comparison - Normal Bulb

Light Comparison - Sodium Lamp vs Laser

ASCII Representation:

Figure 4.4 - Normal Bulb Light:
    ╱─────╲  (Multiple wavelengths)
   ╱   λ₁  ╲ (spreads in all directions)
  │  λ₂ λ₃ │ 
   ╲  λ₄   ╱
    ╲─────╱

Figure 4.5 - Sodium Lamp (Monochromatic):
    ╱─────╲  (Single wavelength λ)
   ╱   λ   ╲ (spreads in all directions)
  │    λ   │ 
   ╲   λ   ╱
    ╲─────╱

Figure 4.6 - Laser Light:
       ║║║  (Single wavelength λ)
       ║║║  (Parallel, unidirectional)
    ═══╬╬╬═══
       ║║║
       ║║║

(5) Write at least 6 applications of laser light in various fields in detail

Answer:

Applications of LASER:

Medical Field:
- Laser Surgery: Precision cutting in eye surgery (LASIK), tumor removal
- Laser Therapy: Treatment of kidney stones, dental procedures
- Endoscopy: Internal examination using fiber optic cables with laser
- Bloodless Surgery: Cauterization of blood vessels during cutting
Communication:
- Optical Fiber Communication: High-speed internet, telephone networks
- Satellite Communication: Long-distance signal transmission
- Data transfer: Laser beams carry more information than radio waves
Industrial Applications:
- Cutting and Welding: Precision cutting of metals, fabrics, plastics
- Drilling: Making micro-holes in hard materials like diamonds
- Surface Treatment: Heat treatment, hardening of metals
- 3D Printing: Laser sintering and stereolithography
Military and Defense:
- Range Finders: Measuring distance to targets accurately
- Guided Missiles: Laser-guided weapons systems
- LIDAR: Detection and ranging for surveillance
- Anti-missile systems: Destroying incoming projectiles
Scientific Research:
- Spectroscopy: Analyzing material composition
- Holography: Creating 3D images
- Laser Cooling: Cooling atoms to near absolute zero
- Plasma Physics: Creating high-temperature plasmas
Entertainment and Commercial:
- Laser Light Shows: Concerts, events, displays
- Barcode Scanners: Retail checkout systems
- CD/DVD/Blu-ray Players: Reading optical discs
- Laser Printers: High-quality printing
Measurement and Instrumentation:
- Precision Measurement: Interferometry for extremely accurate measurements
- Surveying: Land surveying and construction alignment
- Speed Detection: Traffic speed radars

(6) Describe types of optical fiber in detail

Answer:

Optical fibers are classified based on two criteria:

A. Based on Mode of Propagation:

1. Single Mode Fiber (SMF):

Core diameter: Very small (8-10 μm)
Cladding diameter: 125 μm
Mode: Only one mode (fundamental mode) propagates
Transmission: Light travels straight along the axis
Dispersion: Very low intermodal dispersion
Bandwidth: Very high (>100 GHz)
Distance: Long distance (>50 km)
Cost: Expensive
Applications: Long-haul telecommunications, cable TV, internet backbone

Single Mode Fiber:
    ═══════════════════════►
    ═══════════════════════► (Straight path)
    ═══════════════════════►
    |     Core (8-10μm)    |

2. Multi Mode Fiber (MMF):

Core diameter: Large (50-62.5 μm)
Cladding diameter: 125 μm
Mode: Multiple modes propagate simultaneously
Transmission: Light takes multiple paths (zigzag)
Dispersion: High intermodal dispersion
Bandwidth: Lower than SMF (up to 1 GHz)
Distance: Short distance (<2 km)
Cost: Less expensive
Applications: LANs, short-distance communication, building networks

Multi Mode Fiber:
    ═══╱╲╱╲╱╲╱╲╱╲══► (Multiple paths)
    ═══════════════►
    ══╲╱╲╱╲╱╲╱═════►
    | Core (50-62.5μm) |

B. Based on Refractive Index Profile:

1. Step Index Fiber:

Profile: Uniform refractive index in core, sharp boundary with cladding
Core RI: Constant (n₁)
Cladding RI: Constant (n₂), where n₁ > n₂
Types: Can be single mode or multimode
Dispersion: High in multimode version
Applications: Short-distance, low-cost applications

Refractive Index Profile:
    n₁ |████████|
       |████████|
    n₂ |        |________
       └────────┴────────► radius
          core  cladding

2. Graded Index Fiber:

Profile: Refractive index gradually decreases from center to edge of core
Core RI: Maximum at center, decreases parabolically toward edges
Cladding RI: Constant (n₂)
Types: Always multimode
Dispersion: Lower than step index (paths equalized)
Applications: Medium-distance, higher bandwidth applications

Step Index and Graded Index Fibers

Figure: Comparison of refractive index profiles and light propagation in step-index and graded-index optical fibers

Step Index - Refractive Index Profile:
    n₁ |████████|
       |████████|
    n₂ |        |________
       └────────┴────────► radius
          core  cladding
    
    Light Path: ══╲╱╲╱╲╱══► (zigzag)

Graded Index - Refractive Index Profile:
    n₁ |   ╱══╲   |
       |  ╱    ╲  |
    n₂ | ╱      ╲ |________
       └─────────┴────────► radius
          core   cladding

    Light Path: ══╱══╲══╱══╲══► (sinusoidal)

Comparison Table:

Parameter	Step Index (MM)	Graded Index (MM)	Single Mode
Core Diameter	50-200 μm	50-62.5 μm	8-10 μm
Bandwidth	Low	Medium	Very High
Dispersion	High	Medium	Very Low
Distance	Short	Medium	Long
Cost	Low	Medium	High

(7) Write applications of optical fiber in various fields in detail

Answer:

Optical Fiber Applications

Figure: Optical fiber being used for data transmission based on total internal reflection principle

Applications of Optical Fiber:

1. Telecommunications:

Long-Distance Communication: Intercontinental submarine cables
Telephone Networks: Voice transmission over fiber optic cables
Internet Backbone: High-speed internet infrastructure (FTTH - Fiber to the Home)
Mobile Networks: Backhaul connections between cell towers
Advantages: High bandwidth, low signal loss, immune to electromagnetic interference

2. Medical Field:

Endoscopy: Internal examination of body organs (gastroscopy, colonoscopy)
Laser Surgery: Delivering laser beams precisely to target tissues
Photodynamic Therapy: Cancer treatment using light-activated drugs
Medical Imaging: Fiber optic microscopy and imaging systems
Advantages: Flexibility, minimal invasion, precise light delivery

3. Industrial Applications:

Sensors: Temperature sensors, pressure sensors in harsh environments
Lighting: Fiber optic lighting for displays, decorations, and hazardous areas
Inspection: Inspecting hard-to-reach areas in machinery and structures
Process Control: Monitoring industrial processes in real-time
Advantages: Immunity to electrical noise, safe in explosive environments

4. Military and Defense:

Secure Communication: Difficult to tap, no electromagnetic emission
Battlefield Networks: Lightweight, reliable communication systems
Navigation Systems: Fiber optic gyroscopes for aircraft and missiles
Sonar Systems: Underwater detection and communication
Advantages: Secure, lightweight, resistant to jamming

5. Cable Television (CATV):

Broadcast: Distributing TV signals to multiple subscribers
Video on Demand: High-quality video streaming services
Interactive TV: Two-way communication for interactive services
Advantages: High bandwidth, multiple channels, better picture quality

6. Computer Networking:

Local Area Networks (LANs): High-speed data transfer in offices and campuses
Data Centers: Interconnecting servers and storage systems
Storage Networks: SANs (Storage Area Networks)
Advantages: High data rates, long distances without repeaters

7. Automotive Industry:

Vehicle Networks: Connecting various electronic systems in cars
Safety Systems: ABS, airbag deployment sensors
Entertainment: In-vehicle multimedia distribution
Advantages: Lightweight, immune to electromagnetic interference

8. Aerospace:

Aircraft Systems: Flight control, avionics communication
Spacecraft: Data transmission in satellites
Flight Data Recorders: Black boxes using fiber optic technology
Advantages: Lightweight, reliable in extreme conditions

9. Scientific Research:

Spectroscopy: Delivering light to and from spectrometers
Laser Systems: Beam delivery in laboratories
Astronomy: Connecting telescopes to analysis instruments
Particle Physics: Timing and triggering systems in detectors

10. Oil and Gas Industry:

Downhole Monitoring: Temperature and pressure sensors in oil wells
Pipeline Monitoring: Detecting leaks and intrusions
Seismic Sensing: Distributed acoustic sensing for exploration
Advantages: Operates in high-temperature, high-pressure environments

(8) Explain construction of optical fiber with figure

Answer:

Construction of Optical Fiber:

An optical fiber consists of three main parts:

Optical Fiber Structure

Cross-Sectional View:

    ╔═══════════════════════════════════╗
    ║  Buffer Coating/Sheath/Jacket     ║
    ║    (Protective plastic layer)     ║
    ║  ╔═════════════════════════════╗  ║
    ║  ║      Cladding               ║  ║
    ║  ║   (Glass/Plastic, n₂)       ║  ║
    ║  ║   ┌─────────────────────┐   ║  ║
    ║  ║   │      Core           │   ║  ║
    ║  ║   │  (Glass/Plastic)    │   ║  ║
    ║  ║   │   (n₁ > n₂)         │   ║  ║
    ║  ║   │  ~50-200 μm (MM)    │   ║  ║
    ║  ║   │  ~8-10 μm (SM)      │   ║  ║
    ║  ║   └─────────────────────┘   ║  ║
    ║  ║      ~125 μm diameter       ║  ║
    ║  ╚═════════════════════════════╝  ║
    ║        ~250-900 μm total          ║
    ╚═══════════════════════════════════╝

Longitudinal View:

    ═══════════════════════════════════════►
    Light propagates through core via TIR
    ═══════════════════════════════════════►

Fiber Optic Cable Cross-Section

Figure: Cross-section of a typical telecommunication optical fiber cable showing 6 optical fibers, insulated copper wires, central steel wire for strength, and aluminum sheath

Detailed Structure:

1. Core (Inner Part):

Material: Ultra-pure silica glass (SiO₂) or plastic
Diameter:
- Single mode: 8-10 μm
- Multimode: 50-62.5 μm
Refractive Index: High (n₁ ≈ 1.48-1.50)
Doping: May be doped with germania (GeO₂) to increase refractive index
Function: Carries light signals through total internal reflection

2. Cladding (Middle Part):

Material: Silica glass with lower refractive index
Diameter: 125 μm (standard)
Refractive Index: Lower than core (n₂ ≈ 1.46)
Function:
- Provides optical confinement by reflecting light back into core
- Reduces light loss
- Adds mechanical strength

3. Protective Jacket/Buffer Coating (Outer Part):

Material: Plastic polymer (polyimide, acrylate, or PVC)
Thickness: 250-900 μm
Function:
- Protects fiber from physical damage
- Provides mechanical strength
- Prevents moisture ingress
- Color coding for identification

Additional Layers (in cables):

Strength Members: Kevlar or steel wires for tensile strength
Outer Sheath: Additional plastic covering for environmental protection

Diagram with Light Propagation:

Light Propagation in Optical Fiber

ASCII Representation:

    Incident Light
         ↓
    ╔═══│═══════════════════════╗
    ║   ↓                       ║
    ║  ╔↓═══╲               ╗   ║  
    ║  ║  ═══╲═════╱       ║   ║  Cladding (n₂)
    ║  ║   ═══╲═══╱═══     ║   ║  
    ║  ║    ═══X═══╱       ║   ║  Core (n₁ > n₂)
    ║  ║     ══╱═══════    ║   ║  
    ║  ║      ╱═════════   ║   ║  Cladding (n₂)
    ║  ╚═════════════════════╝  ║
    ║    TIR at core-cladding   ║  Buffer Coating
    ║      interface (θ > θc)   ║
    ╚═══════════════════════════╝
                              →  Output Light

Acceptance Angle and Numerical Aperture:

Acceptance Angle Diagram

Figure: Light ray entering optical fiber at acceptance angle θₐ, showing refraction at fiber end and total internal reflection at core-cladding interface

Acceptance Cone

Figure: Acceptance cone showing the solid angle (2θₐ) within which light can enter and propagate through the fiber

Key Points:

Core has higher refractive index than cladding (n₁ > n₂)
Light is confined to core by total internal reflection
Typical core/cladding ratio determines fiber characteristics
Multiple fibers bundled together form fiber optic cables
The difference in refractive indices (Δn = n₁ - n₂) is small (~0.01-0.02)
Acceptance Angle (θₐ): Maximum angle at which light can enter the fiber and still propagate via TIR
Numerical Aperture (NA): sin θₐ = √(n₁² - n₂²) - measures light-gathering capacity
Larger NA means better light-gathering ability
Typical NA values range from 0.13 to 0.50

(9) Describe advantages of optical fiber over coaxial cable

Answer:

Advantages of Optical Fiber over Coaxial Cable:

1. Higher Bandwidth:

Optical Fiber: Can carry data at rates of Terabits per second (Tbps)
Coaxial Cable: Limited to Megabits to Gigabits per second
Reason: Light has much higher frequency than electrical signals
Impact: Supports more simultaneous communications

2. Lower Signal Attenuation (Loss):

Optical Fiber: 0.2-0.5 dB/km loss
Coaxial Cable: 10-30 dB/km loss
Benefit: Signals travel longer distances without amplification/repeaters
Result: Fewer repeaters needed, lower installation and maintenance costs

3. Immunity to Electromagnetic Interference (EMI):

Optical Fiber: Not affected by electromagnetic fields, radio frequency interference
Coaxial Cable: Susceptible to EMI, crosstalk from nearby cables
Advantage: Cleaner signals, fewer errors
Applications: Suitable for electrically noisy environments (factories, power plants)

4. Higher Security:

Optical Fiber: Difficult to tap without detection; no electromagnetic radiation
Coaxial Cable: Can be tapped easily; radiates electromagnetic signals
Benefit: More secure for sensitive data transmission
Use Cases: Military, banking, government communications

5. Lighter and Smaller:

Optical Fiber: Weighs ~10-20 g/km; diameter ~125 μm
Coaxial Cable: Weighs ~100-300 g/km; diameter ~5-10 mm
Advantages:
- Easier to install in tight spaces
- Lower transportation costs
- More cables in same conduit

6. Non-Conductive:

Optical Fiber: Made of glass/plastic; doesn't conduct electricity
Coaxial Cable: Metal conductor; can conduct electricity
Benefits:
- No spark hazard in flammable environments
- No ground loop problems
- Safe during lightning strikes
- Can be used in high-voltage environments

7. Better Signal Quality:

Optical Fiber: Digital signals maintain integrity over long distances
Coaxial Cable: Analog signals degrade with distance
Result: Less signal distortion, better data integrity

8. Longer Distance Transmission:

Optical Fiber: Up to 100+ km without repeaters
Coaxial Cable: Maximum ~1-2 km without amplification
Benefit: Reduced infrastructure costs

9. Corrosion Resistance:

Optical Fiber: Glass/plastic not affected by moisture, chemicals
Coaxial Cable: Metal conductors can corrode
Longevity: Longer lifespan in harsh environments

10. Future-Proof:

Optical Fiber: Bandwidth can be upgraded without changing cables (upgrade equipment only)
Coaxial Cable: Limited upgrade potential
Economic: Better long-term investment

Comparison Table:

Feature	Optical Fiber	Coaxial Cable
Bandwidth	Very High (Tbps)	Moderate (Mbps-Gbps)
Attenuation	0.2-0.5 dB/km	10-30 dB/km
Distance	100+ km	1-2 km
EMI Immunity	Excellent	Poor
Weight	Light (~10-20 g/km)	Heavy (~100-300 g/km)
Size	Small (125 μm)	Large (5-10 mm)
Security	Very High	Low
Cost	Higher initial	Lower initial
Installation	Requires expertise	Easier
Durability	High	Moderate

Disadvantages of Optical Fiber:

Higher initial installation cost
Requires specialized equipment and training
More fragile (glass fibers can break)
Difficult to splice and terminate
Cannot carry electrical power (unlike copper)

Part C: Numerical Solutions (3 marks)

(1) Velocity of light in air is 3 × 10⁸ m/s and in liquid 1.8 × 10⁸ m/s, so find out refractive index of liquid

Given:

Velocity of light in air, c = 3 × 10⁸ m/s
Velocity of light in liquid, v = 1.8 × 10⁸ m/s

To Find:

Refractive index of liquid, n = ?

Formula:

n = c / v

Solution:

n = c / v
n = (3 × 10⁸) / (1.8 × 10⁸)
n = 3 / 1.8
n = 1.67

Answer: The refractive index of the liquid is 1.67

(2) Velocity of light in air is 3 × 10⁸ m/s and in glass 2 × 10⁸ m/s, so find out refractive index of glass

Given:

Velocity of light in air, c = 3 × 10⁸ m/s
Velocity of light in glass, v = 2 × 10⁸ m/s

To Find:

Refractive index of glass, n = ?

Formula:

n = c / v

Solution:

n = c / v
n = (3 × 10⁸) / (2 × 10⁸)
n = 3 / 2
n = 1.5

Answer: The refractive index of the glass is 1.5

(3) Light enters in glass medium from air. Glass has refractive index is 1.56. So find velocity of light in glass

Given:

Velocity of light in air, c = 3 × 10⁸ m/s
Refractive index of glass, n = 1.56

To Find:

Velocity of light in glass, v = ?

Formula:

n = c / v
Therefore, v = c / n

Solution:

v = c / n
v = (3 × 10⁸) / 1.56
v = 1.923 × 10⁸ m/s

Answer: The velocity of light in glass is 1.923 × 10⁸ m/s or 1.92 × 10⁸ m/s

(4) One optical fiber has value of refractive indices are 1.563 and 1.498, respectively. Calculate acceptance angle of optical fiber

Given:

Refractive index of core, n₁ = 1.563
Refractive index of cladding, n₂ = 1.498
Refractive index of air, n₀ = 1

To Find:

Acceptance angle, θₐ = ?

Formulas:

Numerical Aperture (NA) = √(n₁² - n₂²)
Acceptance Angle: sin θₐ = NA / n₀

Solution:

Step 1: Calculate Numerical Aperture (NA)

NA = √(n₁² - n₂²)
NA = √(1.563² - 1.498²)
NA = √(2.4430 - 2.2440)
NA = √0.1990
NA = 0.446

Step 2: Calculate Acceptance Angle

sin θₐ = NA / n₀
sin θₐ = 0.446 / 1
sin θₐ = 0.446
θₐ = sin⁻¹(0.446)
θₐ = 26.5°

Answer:

Numerical Aperture (NA) = 0.446
Acceptance Angle (θₐ) = 26.5°

(5) An optical fiber has value of refractive indices are 1.48 and 1.45, respectively. Calculate acceptance angle and numerical aperture of optical fiber

Given:

Refractive index of core, n₁ = 1.48
Refractive index of cladding, n₂ = 1.45
Refractive index of air, n₀ = 1

To Find:

Numerical Aperture (NA) = ?
Acceptance angle, θₐ = ?

Formulas:

Numerical Aperture (NA) = √(n₁² - n₂²)
Acceptance Angle: sin θₐ = NA / n₀

Solution:

Step 1: Calculate Numerical Aperture (NA)

NA = √(n₁² - n₂²)
NA = √(1.48² - 1.45²)
NA = √(2.1904 - 2.1025)
NA = √0.0879
NA = 0.2965
NA ≈ 0.297

Step 2: Calculate Acceptance Angle

sin θₐ = NA / n₀
sin θₐ = 0.297 / 1
sin θₐ = 0.297
θₐ = sin⁻¹(0.297)
θₐ = 17.27°
θₐ ≈ 17.3°

Answer:

Numerical Aperture (NA) = 0.297 or 0.30
Acceptance Angle (θₐ) = 17.3°

Note: Numerical Aperture (NA) is an important parameter that indicates:

The light-gathering capacity of the optical fiber
The larger the NA, the more light can enter the fiber
Maximum half-angle at which light can enter the fiber core

Additional Important Formulas

Refractive Index

n = c / v = sin i / sin r = λ₀ / λₘ

Critical Angle

sin θc = n₂ / n₁  (where n₁ > n₂)

Numerical Aperture

NA = √(n₁² - n₂²) = n₀ sin θₐ

Where:

n₁ = core refractive index
n₂ = cladding refractive index
n₀ = refractive index of medium from which light enters (usually air, n₀ = 1)
θₐ = acceptance angle

Fractional Refractive Index Change

Δ = (n₁ - n₂) / n₁

For small Δ

NA ≈ n₁√(2Δ)

End of Solutions