Is it correct to say: Using β = λ/d instead of λD/d?

Fringe width is λD/d — do not drop the D.

Is it correct to say: Interchanging the conditions for diffraction minima (a sinθ = nλ) and interference maxima (d sinθ = nλ)?

Interference maxima: d sinθ = nλ (n = 0, 1, 2, ...); diffraction MINIMA: a sinθ = nλ (n ≠ 0).

Is it correct to say: Applying Malus's law directly to unpolarised light?

First polariser reduces intensity by half (I → I/2); Malus's law applies to the polarised beam from then on.

Is it correct to say: Forgetting the factor 2 in the width of the central diffraction maximum?

W = 2λD/a. It is twice the width of a secondary maximum.

Is it correct to say: Confusing coherent sources with monochromatic sources?

Coherent = constant phase difference. Monochromatic = single frequency. Coherence is stricter.

Is it correct to say: Using degrees in cos²θ when calculator is in radians (or vice versa)?

Match calculator mode to units. Common numerical error.

Wave Optics

Huygens principle, interference, diffraction, polarisation — Maharashtra HSC Physics Ch 7

📐 12 formulas✏️ 3 examples🎯 5 practice⚖️ 5 marks🏫 Maharashtra State Board📚 Class 12✓ 2025–26 syllabus

💡

Board Exam Tips

→Derivation of the fringe width formula for Young's double-slit experiment (β = λD/d) is asked in almost every HSC paper for 4 marks.
→State and prove Malus's law (I = I₀cos²θ) for a 2-mark question — this is Maharashtra Board specific.
→Diffraction at a single slit — condition for minima (a sinθ = nλ) and central maximum width — is a favourite 3-marker.
→Distinguish clearly between interference (two coherent sources) and diffraction (single wavefront) — HSC frequently asks the comparison.
→State Huygens' principle before deriving anything — it earns the introductory mark.

📐 Formulas(12)

Huygens' Principle★ Board fav

Every point on a wavefront is a source of secondary wavelets. New wavefront = envelope.

Path Difference for Interference

Δ x = d sin θ \approx \frac{d y}{D}

Conditions for Bright and Dark Fringes★ Board fav

Δ x = nλ (bright), Δ x = (n + \frac{1}{2}) λ (dark)

Fringe Width★ Board fav

β = \frac{λ D}{d}

Intensity in Two-Source Interference

I = I_{1} + I_{2} + 2 I_{1} I_{2} cos ϕ

Ratio of Max to Min Intensity

\frac{I _{ma x}}{I _{min}} = (\frac{I _{1} + I _{2}}{I _{1} - I _{2}})^{2}

Single-Slit Diffraction Minima★ Board fav

a sin θ = nλ, n = \pm 1, \pm 2, \dots

Width of Central Diffraction Maximum

W = \frac{2 λ D}{a}

Malus's Law★ Board fav

I = I_{0} cos^{2} θ

Brewster's Law★ Board fav

tan i_{B} = n_{2} / n_{1}

Resolving Power of a Microscope

RP = \frac{2 μ s i n θ}{λ}

Resolving Power of a Telescope

RP = \frac{D}{1.22 λ}

✏️ Solved Examples

1Solved Exampleeasy3 steps

In Young's double-slit experiment, slit separation is 0.5 mm, screen distance is 1 m, and wavelength of light is 600 nm. Find the fringe width.

Note quantities in SI units.

d = 5 \times 1 0^{- 4} m, D = 1 m, λ = 6 \times 1 0^{- 7} m

2Solved Exampleboard3 steps

Two coherent sources produce intensities in the ratio 4 : 1. Find the ratio of maximum to minimum intensity in the interference pattern.

Amplitudes are proportional to √I.

\frac{a _{1}}{a _{2}} = \frac{I _{1}}{I _{2}} = 4 = 2

3Solved ExampleHOTS4 steps

Unpolarised light of intensity I₀ passes through three polarisers with successive axes at 30° to each other. Find the intensity emerging from the third polariser.

After the first polariser, half the intensity emerges.

I_{1} = I_{0} /2

⚠️ Traps & Common Mistakes

⚠️Common Mistakes6

1
Using β = λ/d instead of λD/d
✓Fringe width is λD/d — do not drop the D.
2
Interchanging the conditions for diffraction minima (a sinθ = nλ) and interference maxima (d sinθ = nλ)
✓Interference maxima: d sinθ = nλ (n = 0, 1, 2, ...); diffraction MINIMA: a sinθ = nλ (n ≠ 0).
3
Applying Malus's law directly to unpolarised light
✓First polariser reduces intensity by half (I → I/2); Malus's law applies to the polarised beam from then on.
4
Forgetting the factor 2 in the width of the central diffraction maximum
✓W = 2λD/a. It is twice the width of a secondary maximum.
5
Confusing coherent sources with monochromatic sources
✓Coherent = constant phase difference. Monochromatic = single frequency. Coherence is stricter.
6
Using degrees in cos²θ when calculator is in radians (or vice versa)
✓Match calculator mode to units. Common numerical error.

🎯 Practice Yourself

🎯Practice Yourself5 questions

Q1
In YDSE, if wavelength is doubled and slit separation halved, by what factor does fringe width change?
Q2
A single slit of width 0.1 mm is illuminated with light of λ = 500 nm. Find the angular width of the central maximum.
Q3
Find Brewster's angle for glass of refractive index 1.5 (light travelling from air to glass).
Q4
State Huygens' principle and use it to prove the law of reflection.
Q5
In YDSE, sources of intensity ratio 9:1 interfere. Ratio of I_max to I_min?

📝 Notes

Wave Optics — Maharashtra HSC Overview

Chapter 7 of the Balbharati Class 12 Physics textbook covers the wave nature of light — Huygens' principle, interference, diffraction, polarisation, and resolving power.

Maharashtra-specific emphasis

Malus's law derivation is asked frequently for 2 marks. The Balbharati book insists on the amplitude → intensity connection.
Polarisation by scattering and plane of vibration vs plane of polarisation are treated more thoroughly than in NCERT.
The resolving power of microscope and telescope are both in the syllabus with numericals — NCERT keeps it at conceptual level.
Huygens' geometrical construction for reflection and refraction is expected to be drawn — the diagram alone carries 1 mark in a 4-mark derivation.

Common exam themes

Two-slit intensity pattern combined with a single-slit envelope (i.e., the observed YDSE pattern is a product of interference and diffraction).
Direct calculation of Brewster's angle from refractive index — simple 2-marker.
Comparing interference vs diffraction in a tabular answer format.

Numerical tips

Wavelengths are often given in nanometres (1 nm = 10⁻⁹ m). Convert before substituting.
Angles in diffraction problems are usually small; use sinθ ≈ tanθ ≈ θ (in radians).
Unpolarised light: assume half intensity passes the first ideal polariser, and Malus's law applies from the second onwards.