“Two slits interfere, one slit diffracts”
Telling the two apart
Interference needs two sources and gives fringes of equal width and equal brightness. Diffraction comes from one slit and gives a wide bright centre with fading edges.
Class 12 Physics · Gujarat Board, CBSE, GUJCET, JEE and NEET
Wave Optics formulas
Wave optics is where light stops being a ray and becomes a wave. Young's double slit gives the standard derivation and the standard numerical, and the difference between interference and diffraction is a theory question asked almost every year.
13 formulas, 4 memory hooks, and the 5 mistakes that cost the most marks.
Interference
| What | Formula | Symbols and notes |
|---|---|---|
| Path difference for maxima | Δ = nλ | bright fringe, n = 0, 1, 2, … |
| Path difference for minima | Δ = (2n − 1)λ/2 | dark fringe |
| Fringe width | β = λD/d | D slit-to-screen distance, d slit separation |
| Position of the nth bright fringe | yn = nλD/d | measured from the central maximum |
| Intensity | I = I₁ + I₂ + 2√(I₁I₂)cosφ | maximum when the waves are in step |
| Ratio of maximum to minimum | Imax/Imin = (√I₁ + √I₂)²/(√I₁ − √I₂)² | in terms of amplitudes, ((a₁ + a₂)/(a₁ − a₂))² |
| In a medium | β' = β/n | the fringes crowd together |
Diffraction and polarisation
| What | Formula | Symbols and notes |
|---|---|---|
| First minimum, single slit | a sinθ = λ | a is the slit width |
| Width of the central maximum | 2λD/a | twice as wide as the other maxima |
| Resolving power of a telescope | θ = 1.22λ/D | the smaller the angle, the better |
| Malus's law | I = I₀cos²θ | θ between the polariser and analyser axes |
| Brewster's law | tan ip = n | the reflected light is fully polarised at this angle |
| Unpolarised through one polaroid | I = I₀/2 | half the intensity always gets through |
Taught by Darshit Bhatt, founder and lead faculty at Darshit Sir Institute. Instrumentation and Control engineer, with a master's degree and a chartered degree, teaching in Paldi, Ahmedabad since 2006.
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Memory hooks
How to remember this chapter.
“Wider slit, narrower pattern”
Single slit diffraction
The central maximum width is 2λD/a, so a wider slit gives a narrower pattern. Everything in diffraction is inverse to what feels natural.
“Half goes through the first”
Unpolarised light and polaroids
An unpolarised beam loses exactly half its intensity at the first polaroid. Malus's law only applies from the second one onwards.
“Only transverse waves polarise”
What polarisation proves
Sound cannot be polarised and light can, which is the evidence that light is a transverse wave.
Where marks go
The mistakes that cost the most.
- Applying Malus's law to the first polaroid with unpolarised light. That one simply halves the intensity.
- Mixing the conditions for maxima and minima. Interference maxima need a whole number of wavelengths of path difference.
- Forgetting that the central diffraction maximum is twice the width of the others.
- Thinking interference creates energy at the bright fringes. It only redistributes it, which is why dark fringes exist.
- Using the air value of wavelength when the apparatus is immersed in a liquid.
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