Physical Optics Examination (With Comprehensive explanations and calculations)

UMOJA WA WAZAZI TANZANIA
WARI SECONDARY SCHOOL

PHYSICS-2: PHYSICAL OPTICS
Paper 131/1

Time: 2:00hrs
March 2021

Question 1: Interference and Thin Films

(a) Applications of Newton's Rings

1. Surface Quality Testing: Used to measure the flatness of optical surfaces by analyzing ring patterns.
2. Wavelength Determination: Can calculate light wavelength by measuring ring diameters and lens curvature.
3. Refractive Index Measurement: Used to determine refractive indices of transparent materials.

(b)(i) Thin Film Path Difference

[Diagram showing light rays reflecting off thin film with angles θ]

For a thin film of thickness t and refractive index n:

Path difference = 2nt cosθ
Where:
• 2 accounts for double traversal of film
• n is refractive index
• t is film thickness
• θ is angle of refraction in film

(b)(ii) Air Wedge Calculation

Given: λ = 5.6×10⁻⁷ m, fringe separation = 1.2 mm = 1.2×10⁻³ m, L = 75 mm = 75×10⁻³ m
For air wedge: β = λ/2α ⇒ α = λ/2β
Wedge angle α = (5.6×10⁻⁷)/(2×1.2×10⁻³) ≈ 2.33×10⁻⁴ rad ≈ 0.013°
Thickness t = L × α = 75×10⁻³ × 2.33×10⁻⁴ ≈ 1.75×10⁻⁵ m = 17.5 μm

(c)(i) Lens Blooming

Blooming: Application of anti-reflection coatings on lens surfaces to reduce light loss through reflection.

(c)(ii) Purpose of Blooming

1. Increases light transmission by reducing surface reflections
2. Improves image contrast by minimizing stray light
3. Protects lens surfaces from scratches and environmental damage

(c)(iii) Blooming Materials

• Magnesium Fluoride (MgF₂)
• Silicon Dioxide (SiO₂)
• Titanium Dioxide (TiO₂)
• Aluminum Oxide (Al₂O₃)

(d)(i) Sonic Boom Definition

Sonic Boom: Shock wave produced when an object moves through air at speeds exceeding the speed of sound, creating a loud explosive noise.

(d)(ii) Sonic Boom Sources

1. Supersonic aircraft (e.g., fighter jets, Concorde)
2. Bullets or projectiles traveling faster than sound
3. Lightning strikes (thunder is a type of sonic boom)
4. Whip cracks (tip exceeds sound speed)

Question 2: Polarization Applications

(a) Polarization Applications

Application	Explanation
Photoelasticity	Measures stress distribution in transparent materials using polarized light patterns
Telecommunication	Fiber optics use polarization to increase channel capacity (polarization multiplexing)
Saccharimetry	Measures sugar concentration by observing rotation of polarized light (optical activity)
Sunglasses	Polarized lenses reduce glare from horizontal reflections (water, roads)

(b) Diffraction Applications

1. CD/DVD Reading: Laser diffraction patterns read microscopic pits on discs
2. Spectroscopy: Diffraction gratings separate light into spectra for analysis
3. X-ray Crystallography: Determines atomic structure using diffraction patterns
4. Holography: Uses interference and diffraction to create 3D images
5. Microscopy: Diffraction limits resolution (Abbe's diffraction limit)

Question 3: Polarized Light

(a) Polarization Concepts

Term	Importance
Dextrorotatory	Substances that rotate polarized light clockwise (right); used in chiral analysis
Levorotatory	Substances that rotate polarized light counterclockwise (left); important in biochemistry
Optically Active	Materials that rotate polarized light; indicates molecular asymmetry/chirality
Double Refraction	Splits light into ordinary/extraordinary rays (birefringence); used in polarizing filters

(b) Differentiations

Comparison	Difference
Polaroid vs Polarimeter	Polaroid is a polarizing filter; polarimeter measures rotation of polarized light
Plane of Vibration vs Polarization	Vibration: plane where E-field oscillates; Polarization: perpendicular to vibration plane
Ordinary vs Polarized Light	Ordinary: random E-field orientations; Polarized: E-field oscillates in single plane

(c) Nicol Prism Construction

1. Made from calcite (CaCO₃) crystal cut diagonally
2. Two pieces cemented with Canada balsam (n=1.55)
3. Works via double refraction: ordinary ray totally internally reflected
4. Emerges as plane-polarized light (extraordinary ray transmitted)

[Diagram showing Nicol prism construction with light paths]

(d) Newton's Ring Observations

Modification	Observation
Front-silvered plate	Increased contrast (brighter fringes) due to higher reflectivity
White light source	Colored fringes (only few visible orders) instead of monochromatic rings
Liquid between lens/plate	Ring diameters decrease (optical path changes with refractive index)