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Wave Optics – Class 12 Physics notes, important questions and MCQs

NCERT Class 12 Physics, chapter 10. Notes, key terms, important questions with answers and MCQs.

Chapter overview

Wave optics explains interference, diffraction and polarisation, which ray optics cannot. Huygens' principle treats every point on a wavefront as a source of secondary wavelets.

Interference

Coherent sources with constant phase difference produce steady fringes.
Young's double slit: fringe width β = λD/d.
Constructive: path difference nλ; destructive: (n + ½)λ.

Diffraction and polarisation

Single slit: first minimum at sin θ = λ/a; central maximum width 2λD/a.
Polarisation proves light is transverse; Malus's law I = I₀ cos²θ.
Brewster's law: tan i_B = n (reflected light fully polarised).

Key terms

Wavefront: locus of points vibrating in the same phase
Coherent sources: sources with a constant phase difference
Huygens' principle: every point on a wavefront acts as a source of secondary wavelets; the new wavefront is their common tangent

Formulas

β = λD/d
I = I₀ cos²θ
tan i_B = n

Important questions with answers

What are coherent sources? Why can't two separate bulbs produce a steady interference pattern?2 marks

Sources with the same frequency and a constant phase difference. Two bulbs emit light with randomly changing phases, so the pattern shifts millions of times a second and averages out.

State Brewster's law and find the polarising angle for glass of refractive index √3.3 marks

At the polarising angle, the reflected light is completely plane polarised and tan i_p = n. For n = √3, tan i_p = √3, so i_p = 60° (reflected and refracted rays are then perpendicular).

Derive the expression for fringe width in Young's double-slit experiment. In an experiment with λ = 600 nm, d = 0.5 mm and D = 1.5 m, find the fringe width and the distance of the third bright fringe from the centre.5 marks

Path difference at a point y from the centre on a screen at distance D: Δ = d sin θ ≈ yd/D. Bright fringes: yd/D = nλ, so yₙ = nλD/d. Dark fringes: (2n − 1)λD/2d. Fringe width β = yₙ₊₁ − yₙ = λD/d. Here β = (6 × 10⁻⁷ × 1.5)/(5 × 10⁻⁴) = 1.8 × 10⁻³ m = 1.8 mm. Third bright fringe: y₃ = 3β = 5.4 mm.

Quick revision

Interference needs coherent sources.
Polarisation shows light is transverse.
Central maximum in diffraction is twice as wide as others.

Exam tips

Fringe width increases with wavelength and screen distance, decreases with slit separation.
Interference needs coherent sources; diffraction is noticeable when the obstacle or slit size is comparable to the wavelength.

Practice MCQs

Polarisation shows that light waves are
1. longitudinal
2. standing waves
3. sound waves
4. transverse
Show answer
Answer: (d) transverse. Transverse.
Steady interference needs
1. incoherent sources
2. coherent sources
3. white light only
4. a single slit only
Show answer
Answer: (b) coherent sources. Constant phase difference.
In YDSE, if the slit separation is doubled, fringe width becomes
1. double
2. half
3. four times
4. same
Show answer
Answer: (b) half. β ∝ 1/d.
Unpolarised light of intensity I₀ passes through a polaroid. Transmitted intensity is
1. I₀
2. zero
3. I₀/4
4. I₀/2
Show answer
Answer: (d) I₀/2. Average of cos²θ is ½.
In YDSE, if the slit separation is doubled, the fringe width becomes
1. double
2. same
3. four times
4. half
Show answer
Answer: (d) half. β = λD/d.
Light of 600 nm, D = 1 m, d = 0.5 mm. Fringe width is
1. 1.2 mm
2. 0.6 mm
3. 0.3 mm
4. 2.4 mm
Show answer
Answer: (a) 1.2 mm. 600 × 10⁻⁹ × 1/(0.5 × 10⁻³).
Brewster angle for glass of n = √3 is
1. 30°
2. 45°
3. 60°
4. 90°
Show answer
Answer: (c) 60°. tan i = √3.
Unpolarised light of intensity I₀ passes through two polaroids at 60°. Final intensity is
1. I₀/2
2. I₀/8
3. I₀/4
4. 3I₀/8
Show answer
Answer: (b) I₀/8. (I₀/2) cos² 60°.

All chapters of Class 12 Physics

Written by Kundali IQ from standard, well-established facts to help with revision. This is not an official NCERT publication; always read your textbook too.