HomePhysics › Q16
PhysicsWave Optics
In interference and diffraction, the light energy is redistributed. If it reduces in one region, producing a dark fringe, it increases in another region, producing a bright fringe.
A. As there is no gain or loss of energy, these phenomena are consistent with the principle of conservation of energy.
B. Diffraction and interference are characteristics exhibited only by light waves.
Choose the correct answer from the options given below:
Options
1
A is true and B is also true
2
A is false, but B is true
3
A is true, but B is false
4
Both A and B are false
Correct Answer
Option 3 : A is true, but B is false
Step-by-Step Solution
A

Statement A — TRUE ✓

In interference and diffraction, energy is not created or destroyed. It is merely redistributed — less energy in dark fringes, more in bright fringes. Average intensity over the whole pattern = 2I₀ = sum of individual intensities. This is perfectly consistent with the law of conservation of energy.

B

Statement B — FALSE ✗

Diffraction and interference are NOT exclusive to light. They are general wave phenomena exhibited by all waves — sound, water, radio, X-rays, and even matter waves (electrons). The Davisson-Germer experiment proved electron diffraction. Statement B is incorrect.

Conclusion: A is true, B is false → Option 3

Theory: Interference, Diffraction & Energy
1. Energy Conservation in Interference

A common misconception is that energy is destroyed in dark fringes of an interference pattern. This is incorrect. The total energy falling on the screen remains constant — it is simply redistributed. Dark fringes (zero intensity) are compensated by brighter bright fringes (intensity 4I₀ instead of 2I₀). Mathematically: average intensity = (I_max + I_min)/2 = (4I₀ + 0)/2 = 2I₀ = sum of individual intensities (I₀ + I₀). Energy is conserved.

2. Wave Nature — Not Exclusive to Light

Diffraction and interference are properties of all wave phenomena. Sound waves diffract around buildings and interfere to create loud and quiet spots. Water waves from two sources create interference patterns visible on the water surface. Radio waves diffract around mountains. X-rays diffract off crystal lattice planes (X-ray crystallography). Electrons diffract off nickel crystals (Davisson-Germer). Neutrons are diffracted in nuclear reactors. Claiming these phenomena are exclusive to light is a fundamental error.

3. Difference: Interference vs Diffraction

📌 Interference: Superposition of waves from a finite number of discrete coherent sources. All fringes have equal width and nearly equal intensity (except for diffraction envelope).

📌 Diffraction: Superposition of waves from infinite coherent sources spread across an aperture. Central maximum is twice as wide as secondary maxima. Intensity decreases with order.

📌 Common: Both are superposition phenomena, both require wave nature, both conserve energy.

4. Single Slit Diffraction Pattern

In single slit diffraction, minima occur at asinθ = nλ (n = ±1, ±2...) where a is slit width. The central maximum has double the angular width of secondary maxima. Width of central maximum = 2λD/a. As slit width decreases, diffraction becomes more prominent and the central maximum widens. For a = λ, light spreads in almost all directions.

5. Conditions for Observing Diffraction

Diffraction is significant when the size of the obstacle or aperture is comparable to the wavelength of the wave. For light (λ ~ 500 nm), a slit must be of micron width to show clear diffraction. Sound (λ ~ 0.1–10 m) diffracts easily around everyday objects. This is why we can hear sound around corners but cannot see around them — light's wavelength is too small relative to everyday obstacles.

6. Resolving Power and Diffraction Limit

Diffraction limits the resolving power of optical instruments. Two closely spaced objects can be resolved only if their diffraction patterns are sufficiently separated (Rayleigh's criterion: minimum resolvable angle θ = 1.22λ/D, where D is aperture diameter). Larger telescope mirrors (larger D) resolve finer details — this is why astronomers build large telescopes.

Frequently Asked Questions
1. Is energy destroyed in dark fringes of interference?
No. Energy is redistributed, not destroyed. The energy "missing" from dark fringes appears in the bright fringes. Total energy on screen = total energy incident on both slits. This is energy conservation in action.
2. Do sound waves show interference?
Yes. Sound waves from two speakers playing the same frequency can interfere. Standing in the room, you can find spots of loudness (constructive) and quietness (destructive). This is the same principle as YDSE for light.
3. Can matter waves show diffraction?
Yes. The Davisson-Germer experiment showed electron diffraction from nickel crystals. Neutron diffraction is used in solid-state physics to study crystal structures. Even atoms have been shown to diffract through microscopic gratings.
4. What is the condition for diffraction to be observable?
Diffraction is significant when the wavelength (λ) is comparable to the size of the aperture or obstacle (a). When a >> λ, diffraction effects are negligible and light travels in straight lines (geometric optics valid).
5. How does interference differ from diffraction practically?
Interference uses two or more discrete coherent sources. Diffraction uses a single extended source (slit, edge, aperture). In practice, both occur simultaneously — the YDSE pattern is actually an interference pattern modulated by a single-slit diffraction envelope.
6. Why is central maximum in single-slit diffraction twice as wide?
Minima in single-slit pattern are at asinθ = ±λ, ±2λ... The first minimum is at sinθ = ±λ/a on both sides. So the central maximum spans from −λ/a to +λ/a — twice the width of secondary maxima which span from nλ/a to (n+1)λ/a.
7. What is Huygens' principle?
Huygens' principle states that every point on a wavefront acts as a secondary source of spherical wavelets. The new wavefront is the envelope of all these secondary wavelets. This principle explains both reflection, refraction, and diffraction of waves.
8. Can radio waves interfere?
Yes. Radio wave interference causes "multipath fading" in telecommunications — when a direct signal and a reflected signal arrive at an antenna with a path difference of λ/2, they cancel. This is why some spots have poor radio/TV reception.
Previous Questions
Q.
YDSE path difference λ gives intensity K – intensity at path difference λ/3
Wave Optics · Answer: K/4
Q.
Sum of KE and PE of simple pendulum bob is 0.02 J – speed at equilibrium position
Oscillations · Answer: 1.41 m/s
Q.
Work done to raise mass m from Earth surface to height equal to radius R
Gravitation · Answer: mgR/2
Q.
Box of mass 15 kg on trolley, static friction 0.12 – maximum acceleration of trolley
Laws of Motion · Answer: 1.2 m/s²
Q.
Hydrogen atom first excited state energy −3.4 eV – radial distance from nucleus
Atoms & Nuclei · Answer: 2.1 × 10⁻¹⁰ m