NCERT Solutions for Class 12 Physics Chapter 10 Wave Optics
NCERT Solutions for Class 12 Physics Chapter 10 Wave Optics covers Huygens' wave theory, wave front construction, refraction and reflection derivations using wave theory, coherent sources, Young's double-slit interference, single-slit diffraction, and polarisation phenomena.
Overview of Topics & Subtopics (Click to Jump)
1. Huygens Principle, Reflection & Refraction of Wavefronts
Short Note:
• Wavefront: The locus of all points in a medium oscillating in the same phase. Types: Spherical wavefront (point source), Cylindrical wavefront (line source), and Plane wavefront (distant source).
• Huygens' Principle:
1. Every point on a given primary wavefront acts as a fresh source of secondary disturbance called secondary wavelets.
2. Secondary wavelets spread out in all directions with the speed of light in that medium.
3. The forward envelope tangent to these secondary wavelets at any later time gives the new position of the wavefront.
• Refraction using Wave Theory: Derivation yields Snell's Law: sin i / sin r = v₁ / v₂ = n₂₁. Note that frequency f remains unchanged, but wavelength changes: λ₂ = λ₁ / n.
• Reflection using Wave Theory: Derivation yields the law of reflection: angle of incidence (i) = angle of reflection (r).
2. Coherent Sources & Young's Double Slit Experiment (YDSE)
Short Note:
• Coherent Sources: Two light sources that emit light waves of the same frequency/wavelength with a constant or zero phase difference over time. Two independent physical sources can never be coherent.
• Interference of Light: Redistribution of light energy due to superposition of two coherent light waves.
• Conditions for Interference:
- Constructive Interference (Bright Fringes): Path difference Δx = n λ (where n = 0, 1, 2...). Maximum Intensity I_max = (√I₁ + √I₂)².
- Destructive Interference (Dark Fringes): Path difference Δx = (2n - 1) (λ / 2) (where n = 1, 2, 3...). Minimum Intensity I_min = (√I₁ - √I₂)².
• Fringe Width (β): Distance between two consecutive bright or dark fringes: β = (λ D) / d, where D is screen distance and d is slit separation.
3. Diffraction of Light & Polarisation
Short Note:
• Diffraction: Bending of light waves around corners or obstacles and spreading into the geometrical shadow region.
• Single Slit Diffraction Pattern:
- Minima Condition: a sin θ = n λ (where a is slit width and n = 1, 2, 3...).
- Secondary Maxima Condition: a sin θ = (2n + 1) (λ / 2).
- Width of Central Maximum: β₀ = (2 λ D) / a (twice the width of secondary fringes).
• Polarisation: The phenomenon of restricting the electric field oscillations of light waves to a single plane perpendicular to propagation direction (proves transverse nature of light).
• Malus's Law: Intensity of polarized light transmitted through an analyzer: I = I₀ cos² θ.
• Brewster's Law (Polarisation by Reflection): At Brewster's angle i_B, reflected light is completely plane-polarized and reflected ray is perpendicular to refracted ray: tan i_B = n.
Intext & Conceptual Questions
• Coherent Sources: Two sources of light are said to be coherent if they emit light waves having the same frequency, same wavelength, and maintaining a zero or constant phase difference between them.
• Why independent sources fail: Light is emitted by independent sources due to rapid and random atomic transitions lasting about 10⁻⁸ s. Independent sources undergo continuous, random phase fluctuations relative to each other. As a result, the interference pattern shifts positions millions of times per second, washing out the fringes and giving an average uniform intensity on the screen.
| Feature | Interference | Diffraction |
|---|---|---|
| Source of Origin | Superposition of waves from two distinct coherent sources. | Superposition of secondary wavelets originating from different parts of the same wavefront. |
| Width of Fringes | All bright and dark fringes are generally of equal width (β). | Fringes are of unequal width; central maximum is twice as wide as secondary maxima. |
| Intensity distribution | All bright fringes have equal intensity. | Central maximum has peak intensity; secondary maxima rapidly decrease in brightness. |
| Dark Region Contrast | Dark fringes are usually completely dark (zero intensity). | Minima are not completely dark. |
Textbook Chapter End Exercise Questions
Given:
• Wavelength in air (λ_air) = 589 nm = 589 × 10⁻⁹ m
• Refractive index of water (n) = 1.33
• Speed of light in vacuum (c) = 3.0 × 10⁸ m/s
Part (a): Frequency (f) of Refracted Light
Frequency depends strictly on the light source and remains unchanged during refraction.
f = c / λ_air = (3.0 × 10⁸) / (589 × 10⁻⁹) ≈ 5.09 × 10¹⁴ Hz
Part (b): Speed of Refracted Light (v)
v = c / n = (3.0 × 10⁸) / 1.33 ≈ 2.26 × 10⁸ m/s
Part (c): Wavelength of Refracted Light (λ_water)
λ_water = λ_air / n = 589 / 1.33 ≈ 442.86 nm
• Frequency = 5.09 × 10¹⁴ Hz
• Speed in water = 2.26 × 10⁸ m/s
• Wavelength in water = 442.86 nm
Given:
• Slit separation (d) = 0.28 mm = 0.28 × 10⁻³ m
• Distance to screen (D) = 1.4 m
• Order of fringe (n) = 4
• Distance of 4th bright fringe (y₄) = 1.2 cm = 1.2 × 10⁻² m
Step 1: Formula for Position of Bright Fringe
y_n = (n λ D) / d
Step 2: Calculate Wavelength (λ)
λ = (y₄ × d) / (4 × D)
λ = (1.2 × 10⁻² × 0.28 × 10⁻³) / (4 × 1.4)
λ = (0.336 × 10⁻⁵) / 5.6 = 6.0 × 10⁻⁷ m = 600 nm
The wavelength of light used in the experiment is 600 nm (or 6.0 × 10⁻⁷ m).
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