Wave Optics — Class 12 Physics NCERT Solutions (Free)

Free step-by-step NCERT solutions for Class 12 Physics chapter "Wave Optics" — 7 important questions with detailed answers for CBSE board exam preparation.

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TL;DR: Free step-by-step NCERT solutions for Class 12 Physics chapter "Wave Optics" — 7 important questions with detailed answers for CBSE board exam prepara…

Written & reviewed by the Syllab.in Academic Team (CBSE/NCERT subject experts) · Updated Jul 23, 2026

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Key Questions Covered:

Explain Huygens' principle and show how it accounts for reflection and refrac…
What is interference? Derive the condition for constructive and destructive i…
In Young's double slit experiment, the slits are 1 mm apart and screen is 1 m…
Define diffraction and explain single slit diffraction pattern. Derive the co…
What is diffraction grating? Derive the grating equation and explain its appl…
A diffraction grating has 4000 lines per cm. Find angles of first and second …
+ 1 more questions in the full chapter

Solutions Summary:

Question	Status
Explain Huygens' principle and show how it accounts for r…	✓ Solved
What is interference? Derive the condition for constructi…	✓ Solved
In Young's double slit experiment, the slits are 1 mm apa…	✓ Solved
Define diffraction and explain single slit diffraction pa…	✓ Solved
What is diffraction grating? Derive the grating equation …	✓ Solved
A diffraction grating has 4000 lines per cm. Find angles …	✓ Solved

Showing 6 of 7 questions

Q1: Explain Huygens' principle and show how it accounts for reflection and refraction.

Huygens' Principle: Every point on a wavefront acts as a source of secondary wavelets, and the new wavefront is the envelope of these secondary wavelets. Reflection using Huygens' Principle: - Incident plane waves AB fall on plane surface MM' - Each point on AB generates secondary wavelets - At time t, point A has traveled distance d₁, point B has traveled distance d₂ - Secondary wavelets form reflected wave A'B' - Angle of incidence = Angle of reflection (proven from geometry) - Reflected ray ...

Q2: What is interference? Derive the condition for constructive and destructive interference in Young's double slit experiment.

Interference: Superposition of two coherent waves resulting in maximum or minimum intensity. Young's Double Slit Experiment: Two slits S₁ and S₂ separated by distance d Distance to screen: D >> d Wavelength: λ Path difference at point P on screen: Δ = S₂P - S₁P ≈ d sin θ ≈ d × y/D Where y = distance from center on screen Phase difference: δ = 2π/λ × Δ = 2πdy/(λD) Constructive Interference (Bright fringes): Path difference = nλ (n = 0, 1, 2, ...) Δ = nλ dy/D = nλ y_n = nλD/d Phase diff...

Q3: In Young's double slit experiment, the slits are 1 mm apart and screen is 1 m away. Light of wavelength 500 nm is used. Find fringe width and position of 3rd bright fringe.

Given: Slit separation: d = 1 mm = 10⁻³ m Distance to screen: D = 1 m Wavelength: λ = 500 nm = 500 × 10⁻⁹ m = 5 × 10⁻⁷ m Fringe width: β = λD/d β = (5 × 10⁻⁷ × 1)/(10⁻³) β = 5 × 10⁻⁴ m = 0.5 mm Position of 3rd bright fringe (n = 3, counting from center at n = 0): For bright fringes: y_n = nλD/d For 3rd bright fringe: y₃ = 3λD/d y₃ = 3 × (5 × 10⁻⁷) × 1 / (10⁻³) y₃ = (15 × 10⁻⁷) / (10⁻³) y₃ = 15 × 10⁻⁴ m = 1.5 mm Alternatively using fringe width: y₃ = 3β = 3 × 0.5 = 1.5 mm Answers: - Fringe wi...

Q4: Define diffraction and explain single slit diffraction pattern. Derive the condition for minima.

Diffraction: Bending of light around obstacles or edges, caused by wave nature of light. Produces pattern of bright and dark bands. Single Slit Diffraction: Slit of width 'a' acts as source of secondary wavelets Screen at large distance D from slit Condition for Minima (Dark bands): Divide slit into two halves of width a/2 Path difference between rays from top and bottom = (a/2) sin θ For first minimum: Path difference = λ/2 (a/2) sin θ₁ = λ/2 a sin θ₁ = λ For nth minimum: Path difference = ...

Q5: What is diffraction grating? Derive the grating equation and explain its applications.

Diffraction Grating: Optical component with large number of closely-spaced slits (or rulings) producing multiple beams of light. Grating Equation Derivation: Consider N slits separated by distance d (grating spacing) Light of wavelength λ incident normally on grating Path difference between adjacent slits = d sin θ For constructive interference: Path difference = nλ d sin θ = nλ (n = 0, 1, 2, ...) Grating Equation: d sin θ = nλ Where: d = distance between adjacent slits (grating spacing) θ = ...

Q6: A diffraction grating has 4000 lines per cm. Find angles of first and second order maxima for light of wavelength 550 nm.

Given: Number of lines per cm = 4000 lines/cm Wavelength λ = 550 nm = 550 × 10⁻⁹ m Grating spacing: d = 1/(4000 × 10² lines/m) = 1/(4 × 10⁵ lines/m) d = 2.5 × 10⁻⁶ m = 2500 nm Using grating equation: d sin θ = nλ sin θ = nλ/d For first order (n = 1): sin θ₁ = (1 × 550 × 10⁻⁹)/(2.5 × 10⁻⁶) sin θ₁ = 550/(2.5 × 10³) = 550/2500 = 0.22 θ₁ = sin⁻¹(0.22) ≈ 12.7° For second order (n = 2): sin θ₂ = (2 × 550 × 10⁻⁹)/(2.5 × 10⁻⁶) sin θ₂ = 1100/2500 = 0.44 θ₂ = sin⁻¹(0.44) ≈ 26.1° Verification of maxim...

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