"Wave Phenomena and Light"

About

Light behaves both as a particle and as a wave. This chapter explores the wave nature of light — how wavefronts propagate, how light waves interfere with each other, and how Young's double-slit experiment provided the first conclusive evidence for the wave theory of light.

Key Concepts

22.1 Wavefronts and Huygens' Principle

A wavefront is a surface where all points are in the same phase of oscillation.

Wavefront is always perpendicular to the direction of wave propagation
Spherical wavefront: From a point source — rays are radial
Plane wavefront: From a distant source — rays are parallel

Huygens' principle: Every point on a wavefront acts as a source of secondary wavelets. The envelope of these wavelets gives the new wavefront.

Wavelet radius at time $t$ : $r = v t$ . Ratio of radii at $t = 3$ s and $t = 6$ s = $3 : 6 = 1 : 2$ .

22.2 Interference of Light

When two waves superpose, the resultant displacement depends on:

Amplitude of each wave
Phase difference between them

Constructive interference: Waves arrive in phase → bright fringe. Path difference = $nλ$ ( $n = 0, 1, 2, \dots$ )

Destructive interference: Waves arrive out of phase → dark fringe. Path difference = $(2 n + 1) λ /2$

22.3 Young's Double-Slit Experiment

Demonstrated the wave nature of light through interference.

Fringe width: $β = \frac{λ D}{d}$

Where $D$ = distance to screen, $d$ = slit separation, $λ$ = wavelength.

22.4 Coherent Sources

Coherent sources emit waves of:

Same frequency
Same wavelength
Constant phase difference

Two incandescent bulbs are incoherent — random phase → no interference pattern, just uniform illumination. Our eyes also cannot act as coherent sources.

INTEXT QUESTIONS 22.1

Q1. What is the relative orientation of a wavefront and the direction of propagation?

Ans: The wavefront is always perpendicular to the direction of propagation. For a spherical wavefront, rays are radial. For a plane wavefront, rays are parallel and perpendicular to the flat wavefront.

Q2. A source emits wavelets at t = 0. Calculate the ratio of radii of wavelets at t = 3 s and t = 6 s.

Ans: $r = v t$ . Ratio = $v \times 3 : v \times 6 = 3 : 6 = 1 : 2$ . Radius at 6 s is twice that at 3 s.

INTEXT QUESTIONS 22.2

Q1. On what factors does the resultant displacement in superposition depend?

Ans: (i) Amplitude of each wave, (ii) Phase difference between the waves at that point.

Q2. In Young's experiment, how is constructive interference produced?

Ans: When waves from two coherent sources arrive in phase — path difference = $nλ$ ( $n = 0, 1, 2, \dots$ ). Crests align → amplitude is maximum → bright fringe.

Q3. If we replace pinholes by two incandescent bulbs, can we observe fringes?

Ans: No. Incandescent bulbs are incoherent sources — random phase, different frequencies. No sustained interference pattern — screen shows uniform illumination.

Q4. What are coherent sources? Can our eyes act as coherent sources?

Ans: Coherent sources emit waves of same frequency, same wavelength, and constant phase difference. Our eyes cannot act as coherent sources — they don't emit light with fixed phase relationships.

Terminal Exercise

State Huygens' principle. Use it to prove the laws of reflection and refraction.
What is interference of light? Distinguish between constructive and destructive interference.
Describe Young's double-slit experiment. Derive the expression for fringe width: $β = λ D / d$ .
In Young's experiment, the slit separation is 0.5 mm and the screen is 2 m away. If the fringe width is 2 mm, find the wavelength of light used.
What are coherent sources? Why are two independent sources of light not coherent?
Explain why a soap bubble appears coloured in sunlight.
State the conditions for sustained interference of light.
In a double-slit experiment, the distance between the slits is doubled. How does the fringe width change?
What is the shape of the interference fringes in Young's experiment? Why?
Two coherent sources of intensity ratio 1:4 interfere. Find the ratio of maximum to minimum intensity.

Quick Revision

Concept	Formula / Key Point
Wavefront	Surface of constant phase, perpendicular to propagation
Huygens' Principle	Every point = source of secondary wavelets
Constructive interference	Path diff = $nλ$
Destructive interference	Path diff = $(2 n + 1) λ /2$
Fringe width	$β = λ D / d$
Coherent sources	Same $ν$ , $λ$ , constant phase diff

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