PHYSICS S5 Unit 13: Interference of Light Waves.

What Will You Learn?

• The course Unit 13: Interference of Light Waves is a crucial unit in Wave Optics that provides definitive evidence for the wave nature of light. It builds upon the basic concepts of waves to analyze how light waves overlap and interact with each other.
• I. Fundamentals of Wave Interference
• This section establishes the basic principles of wave interaction that are then applied to light.
• • Principle of Superposition: The core concept stating that when two or more waves overlap, the resultant displacement at any point is the vector sum of the displacements of the individual waves at that point.
• • Coherence: A critical requirement for sustained, observable interference patterns. Two light sources are coherent if they:
• o Have the same frequency (and wavelength).
• o Maintain a constant phase difference between them over time.
• o In practice, this is achieved by splitting the light from a single source.
• • Types of Interference:
• o Constructive Interference: Occurs when waves meet in phase (path difference is an integer multiple of the wavelength, nλ). The resulting amplitude is maximum, producing bright fringes (maxima).
• o Destructive Interference: Occurs when waves meet out of phase by half a wavelength (path difference is a half-integer multiple of the wavelength, (n + 1/2)\λ). The resulting amplitude is minimum (or zero), producing dark fringes (minima).
• II. Young's Double-Slit Experiment
• This is the most important experiment in this unit, providing the classical proof of the wave nature of light.
• • Experimental Setup: Light from a single source passes through two very narrow, closely spaced slits, acting as two coherent sources.
• • Fringe Pattern: The waves interfere to produce a pattern of alternating bright and dark lines (fringes) on a screen.
• • Interference Conditions and Formulas: You will derive and use the formulas that relate the fringe position (y), wavelength (λ), slit separation (d), and the distance to the screen (D):
• o Bright Fringes (Constructive): d sin θ = nλ
• o Dark Fringes (Destructive): d sin θ = (n + 1/2)\λ
• • Fringe Spacing (Δy): The distance between consecutive bright or dark fringes:
• Δy = λD/d
• III. Interference in Thin Films
• You will apply interference principles to explain colors observed in nature.
• • Mechanism: Interference occurs between light waves reflected from the front surface and the back surface of a thin transparent film (like a soap bubble or an oil slick on water).
• • Phase Change on Reflection: You will learn that a 180o phase shift occurs when light reflects off a boundary leading to a denser medium, which must be accounted for in the path difference calculation.
• • Conditions for Maxima/Minima: The condition for constructive/destructive interference is modified based on the thickness of the film (t), the film's index of refraction (n), and the phase changes on reflection.
• This unit is essential for understanding the physical reality of light as a wave, a concept that immediately precedes the study of quantum mechanics where light's particle nature is explored.