Chapter 26 · Class 11-12 & JEE/NEET
Wave Optics
38 topics in 11 parts
Young's fringe width Wave speed and refractive index Phase difference from path difference Optical path length Two-wave resultant intensity Equal-source interference intensity
Key ideas
4. Systematic Comparison & Parameter Classifications
| Body Shape | Axis of Rotation | Moment of Inertia (I) | Shape Factor (k² / R²) |
|---|---|---|---|
| Thin Ring / Hollow Cylinder | Central Axis Perpendicular to Plane | M R² | 1.0 (Slowest Down Incline) |
| Solid Disc / Solid Cylinder | Central Axis Perpendicular to Plane | (1/2) M R² | 0.50 |
| Solid Sphere | Diameter Axis | (2/5) M R² | 0.40 (Fastest Down Incline) |
| Spherical Shell (Hollow) | Diameter Axis | (2/3) M R² | 0.67 |
| Uniform Rod (Length L) | Through Center Perpendicular to Length | (1/12) M L² | L² / (12 R²) |
Exam Worked Example
Problem: A solid sphere and a solid cylinder of equal mass M and radius R roll down the same inclined plane without slipping from rest. Find the ratio of their accelerations down the incline.
● Step 1: Formula for linear acceleration in pure rolling: a = (g sin θ) / (1 + k²/R²).
● Step 2: For solid sphere, k²/R² = 2/5 = 0.4. Therefore, a_sphere = (g sin θ) / (1 + 2/5) = 5/7 g sin θ ≈ 0.714 g sin θ.
● Step 3: For solid cylinder, k²/R² = 1/2 = 0.5. Therefore, a_cyl = (g sin θ) / (1 + 1/2) = 2/3 g sin θ ≈ 0.667 g sin θ.
● Step 4: Ratio a_sphere / a_cyl = (5/7) / (2/3) = (5 * 3) / (7 * 2) = 15 / 14 ≈ 1.07. The solid sphere reaches the bottom first!
Checkpoint
1. When a ballet dancer pulls her arms inward during a spin on smooth ice, what happens to her kinetic energy?
All 38 topics in Wave Optics
Huygens' Principle & Wavefronts
- Secondary Wavelets & Wavefront Construction
- Types of Wavefronts (Plane, Spherical & Cylindrical)
- Reflection & Refraction Laws
Interference of Light
- Superposition & Resultant Intensity
- Coherent & Incoherent Sources
- Conditions for Sustained Interference
- Division of Wavefront & Amplitude
- Multi-Slit Interference
Young's Double-Slit Experiment
- Position of Bright & Dark Fringes
- Fringe Width
- Intensity Distribution
- Maximum Order of Interference Fringes
- Shape of Interference Fringes
- White-Light Interference
- Oblique Incidence
- Source Beyond Central Line
Geometrical & Optical Paths
- Optical Path & Phase Difference
- Fringe Displacement Due to a Thin Sheet
- Minimum Glass Plate Thickness for Fringe Shift
Thin-Film Interference
- Reflected & Transmitted Interference
- Phase Change on Reflection
- Wedge-Shaped Film Fringes
Fresnel's Biprism
- Virtual Coherent Sources & Fringe Width
- Wavelength & Refractive Index Measurement
Lloyd's Mirror Experiment
- Interference by a Single Mirror
- Phase Change Due to Reflection
Diffraction of Light
- Single-Slit Diffraction
- Minima & Secondary Maxima
- Central Maximum Width & Angular Width
- Fresnel & Fraunhofer Diffraction
Optical Instruments
- Microscopes & Telescopes
- Resolving Power & Rayleigh's Criterion
Polarisation of Light
- Plane-Polarised Light & Transverse Nature
- Brewster's Law & Polarising Angle
- Malus' Law & Polaroid Combinations
- Polarisation by Scattering & Refraction
Doppler Effect in Light
- Redshift & Blueshift
- Doppler Frequency & Wavelength Shift