Unit-4. LASER and Fiber Optics - Short Solutions

Part A: Short Answers (1-2 marks)

(1) Snell's law

The ratio of sine of angle of incidence to sine of angle of refraction is constant.

n₁ sin θ₁ = n₂ sin θ₂  or  sin i/sin r = n₂/n₁

(2) Full form of LASER

Light Amplification by Stimulated Emission of Radiation

(3) Monochromatic and Polychromatic light

Monochromatic: Single wavelength/color (e.g., laser, sodium lamp)
Polychromatic: Multiple wavelengths/colors (e.g., white light, sunlight)

(4) Properties of laser light

Monochromatic (single wavelength)
Coherent (waves in phase)
Directional (highly focused beam)
High intensity
Polarized

(5) Definitions

Absolute Refractive Index: Ratio of speed of light in vacuum to speed in medium.

n = c/v

Critical Angle: Angle of incidence in denser medium for which angle of refraction becomes 90°.

sin θc = n₂/n₁

Part B: Detailed Answers (2-3 marks)

(1) Refraction of light

Change in direction of light when passing from one medium to another due to change in velocity.

Rarer to denser: bends towards normal
Denser to rarer: bends away from normal

(2) Refractive index

Measure of how much light slows in a medium.

Absolute: n = c/v (always > 1)

Examples: Water (1.33), Glass (1.5), Diamond (2.42)

(3) Total Internal Reflection (TIR)

Complete reflection of light back into denser medium when traveling from denser to rarer medium.

Conditions:

Light travels from denser to rarer medium (n₁ > n₂)
Angle of incidence > critical angle (i > θc)

Applications: Optical fibers, prisms, diamonds, mirages

(4) Common light vs Laser light

Property	Common Light	Laser Light
Wavelength	Multiple	Single
Coherence	Non-coherent	Coherent
Direction	All directions	Unidirectional
Intensity	Low	Very high
Source	Spontaneous emission	Stimulated emission

(5) Applications of LASER (6 fields)

Medical: Surgery (LASIK), tumor removal, kidney stones
Communication: Optical fiber networks, data transmission
Industrial: Cutting, welding, drilling, 3D printing
Military: Range finders, guided missiles, LIDAR
Scientific: Spectroscopy, holography, measurements
Commercial: Barcode scanners, CD/DVD players, printers

(6) Types of optical fiber

By Mode:

Single Mode: Core 8-10 μm, long distance, low dispersion
Multimode: Core 50-200 μm, short distance, high dispersion

By Refractive Index:

Step Index: Uniform core RI, zigzag path
Graded Index: RI decreases from center, sinusoidal path

(7) Applications of optical fiber

Telecommunications: Internet, telephone, cable TV
Medical: Endoscopy, laser surgery, imaging
Industrial: Sensors, lighting, inspection
Military: Secure communication, navigation
Networking: LANs, data centers
Automotive: Safety systems, entertainment

(8) Construction of optical fiber

Three layers:

Core: Glass/plastic, high RI (n₁), carries light (8-200 μm)
Cladding: Lower RI (n₂), reflects light back (125 μm)
Jacket: Protective plastic coating (250-900 μm)

Light propagates through TIR at core-cladding interface.

(9) Advantages of optical fiber over coaxial cable

Higher bandwidth: Terabits vs Gigabits per second
Lower loss: 0.2-0.5 dB/km vs 10-30 dB/km
EMI immunity: Not affected by electromagnetic interference
Higher security: Difficult to tap
Lighter and smaller: Easy installation
Non-conductive: No spark hazard, lightning safe
Longer distance: 100+ km without repeaters
Corrosion resistant: Glass/plastic vs metal
Future-proof: Upgradeable without cable change
Lower cost: Cheaper raw materials (silica)

Part C: Numericals (3 marks)

(1) Refractive index of liquid

Given: c = 3×10⁸ m/s, v = 1.8×10⁸ m/s

n = c/v = (3×10⁸)/(1.8×10⁸) = 1.67

Answer: 1.67

(2) Refractive index of glass

Given: c = 3×10⁸ m/s, v = 2×10⁸ m/s

n = c/v = (3×10⁸)/(2×10⁸) = 1.5

Answer: 1.5

(3) Velocity of light in glass

Given: n = 1.56, c = 3×10⁸ m/s

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

Answer: 1.92×10⁸ m/s

(4) Acceptance angle

Given: n₁ = 1.563, n₂ = 1.498

NA = √(n₁² - n₂²) = √(2.443 - 2.244) = √0.199 = 0.446
θₐ = sin⁻¹(0.446) = 26.5°

Answer: NA = 0.446, θₐ = 26.5°

(5) Acceptance angle and NA

Given: n₁ = 1.48, n₂ = 1.45

NA = √(n₁² - n₂²) = √(2.1904 - 2.1025) = √0.0879 = 0.297
θₐ = sin⁻¹(0.297) = 17.3°

Answer: NA = 0.297, θₐ = 17.3°

Key Formulas

Refraction: n = c/v = sin i/sin r
Critical Angle: sin θc = n₂/n₁
TIR Conditions: n₁ > n₂, i > θc
Optical Fiber: C = ε₀A/d
Numerical Aperture: NA = √(n₁² - n₂²)
Acceptance Angle: sin θₐ = NA

Short Solutions - Unit 4